Fractal Journal 1999 ~ 2004 J
Y F
J
Main Contents The Lyapunov Read Me R
User Manual Contents O The Amadeus Page
Editors Statement
The contents pages are not very populated with information however should be done well enough for anyone reading this journal diary to navigate back and forth throughout it. If you mouse over anything that looks like a company name reference for software it should turn into a little hand pointer and will take you to the web location of its source, please be sure to be logged online so that it will take you there. All mention of software in this document are meant solely for reference only and I do not have any professional connection with any of them other than to use their software This document does not represent any suggested software company and the names mentioned are copyright and trademarks of those respective software companies. Please accept this PDF document as reference only as I am not a skilled mathematician... only a FractalDesigner user and the fractals represented here are the culmination of the past three years using FractalDesigner. Please feel free to contact me if you are also a FractalDesigner user so that we can further exchange information regarding the possibilities of FractalDesigner or Amadeus II. Thank you very much! Jerry Baker J. Baker Studio jbakerstudio@earthlink.net
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Fractal Designer Fractal Journal 1999 ~ 2004 J. Baker Studio Keyboard functions used: "option v [√]", "option 0 [º] Look's like a large degree symbol in FD." "option d [∂]", "option { [“]" "option j [∆]", "option i [ˆ]", "Operator [exp]", "option 8 [•]" Button option selected. To apply any of the formulas supplied with the rendered fractal examples Click Here for the suggested methods of applying the data given each fractal.
2
Fractal Designer 2.01 Fractal Journal 1999 ~ 2004 J. Baker Studio
Title: Ariel
[ ]Use precompiled function... (Vivid 03 Color Palette) f(z,x)= sqr(x)+z*sqr(ƒx,ƒe(x))+z/sqrt(ƒx,ƒe)+z)+sqr(x)+z*sqr(ƒx.i,ƒe(x.i))+z/sqrt(sqr(ƒx,ƒe)) Params NMax:100 Eps:0.071 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.025 Center Y:0 Step:0.0001171875 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
3
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Ariel Two
[ ]Use precompiled function... (Vivid 03 Color Palette) f(z,x)= sqr(x)+z*sqrt(ƒx,ƒe(x))+z/sqrt(sqr(ƒx,ƒe)+z)+sqr(x)+z*sqr(ƒx.i,ƒe(x.i))+z/sqrt(sqr(ƒx,ƒe)) Params NMax:100 Eps:0.071 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.025 Center Y:0 Step:0.0001171875 Attractors [•] Constant Re:-1.0 Im:0 Expr:"no data" Palette: "Everything" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
4
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Arm
[ ]Use precompiled function... (Forest Color Palette) f(z,x)= sqr(x)+z Params NMax:1000 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.15435409521484 Center Y:1.0304689804688 Step:4.9886431012835e-08 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
5
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Big Face
[ ]Use precompiled function... (depths Color Palette) f(z,x)= sqrt(cos(sin(z))+(x)+z)/sqr(x) Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.58 Center Y:0.0028571428571428 Step:0.0005994897959183 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette: "Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
6
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Big Spectro
[ ]Use precompiled function... (Vivid 01 Color Palette) f(z,x)= x+(sin(sin(z)/(sqr(x))+√3800))/(√35000-sqr(z)*abs(z)) Params NMax:100 Eps:0.002 [x(0) "√z*sin(i-√02(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.00244375000000003 Center Y:-0.00234375 Step:2.288818359375e-05 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
7
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Big Swill
[ ]Use precompiled function... (Embryo Palette Color Palette) f(z,x)= sqr((cube(x)+4*(c-1)*x+(c-1.5)(c-2))/(3.7sqr(x)+3(c-2)x+sqrt(c)-3c+3)) Params NMax:250 Eps:0.01 [x(0) "z"] "Constant c" Re:0.8642931753 Im:1.453934901 Use fast algorithm[√] Region Center X:-1.71216796875 Center Y:1.613759765625 Step:0.0007389613560267 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
8
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Black Moon
[ ]Use precompiled function... (Vivid 03 Color Palette) f(z,x)= cos(abs(3*e))+(x)+z/e,i-c(sqr(x,sin(∂1.8/2))) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
9
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Blob Connections
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= sqrt(z,abs(c-7))+c(sin(x*2(sqr(e,x)))) Params NMax:200 Eps:0.001 [x(0) "z(2ºπc,e)"] "Constant c" Re:-1.59 Im:3.138944703e-29 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
10
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Broken New
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)+z-sqr(z)+c Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
11
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Catapillar Back “A”
[ ]Use precompiled function... (depths Color Palette) f(z,x)= x-(sin(cos(x))-√0395)/(√65*sqr(x)*cos(x)) Params NMax:100 Eps:0.01 [x(0) "√z*sin(e(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show apprach phases
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FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Catapillar Back “B”
[ ]Use precompile functions... (Rainbow Color Palette) f(z,x)= x-(sin(cos(x))-√4795)/(√45*sqr(x)*cos(x)) Params NMax:100 Eps:0.001 [x(0) "√z*sin(e(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette"Re" Infinity [√]Consider as attractor/Palette:Everything" [√]Show apprach phases
13
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Catapillar Back “C”
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= x-(sin(cos(x))-√1795)/(√65*sqr(x)*cos(x)) Params NMax:100 Eps:0.01 [x(0) "√z*sin(e(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show apprach phases
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FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Catapillar Back “X”
[ ]Use precompile functions... (Vivid 02 Color Palette") f(z,x)= x-(sin(cos(x))-√9000)/(√4000*sqr(x)*cos(x)) Params NMax:100 Eps:0.021 [x(0) "√z*cos(e+√2(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show apprach phases
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FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Catapillar Back “Z”
[ ]Use precompile functions... (Vivid 02 Color Palette) f(z,x)= x-(sin(cos(x))-√9000)/(√1000*sqr(x)*cos(x)) Params NMax:100 Eps:0.021 [x(0) "√z*cos(e(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show apprach phases
16
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Circle One
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)+c(z)+c Params NMax:995 Eps:0.063 [x(0) "z"] "Constant c" Re:-0.040099 Im:0.0074856433 Use fast algorithm[√] Region Center X:6.540098700003e-05 Center Y:-6.4573330000872e-0 Step:0.0028571428571429 Attractors [•] Constant Re:-.2003672109 Im:0.00034567e Expr""no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Yellow" [ ]Show apprach phases
17
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Circle Span
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= sqr(z,x)+z,e(z*5)/inv(1.9/x)sqr(i)abs(sqrt(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.002 Center Y:0.0009999999999999 Step:0.000375 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
18
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Circle Two
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqrt(x)i*(z)i Params NMax:300 Eps:0.021 [x(0) "z"] "Costant c" Re:0.030099 Im:-0.0103485 Use fast algorithm[√] Region Center X:-0.001934599013 Center Y:-6.4573329999762e-0 Step:0.0009508928571428 Attractors [•] Constant Re:-0.020700 Im:0.090363e Expr:"no data" Palette:"Yellow" Infinity [√]Consider as attractor/Palette"Blue" [√]Show approach phases
19
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Covery
[ ]Use precompiled functions... (Vivid 01 Color Pallete) f(z,x)= cos(z+x(1.2))-i Params NMax:300 Eps:0.021 [x(0) "no data"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:10.82 Center Y:0.47 Step:0.0015848214285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
20
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Crucial Point
[ ]Use precompiled functions... (Forest Color Palette) f(z,x)= sqr(x(sin(z*2))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.001 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.071320064484122 Center Y:-0.000968812003968 Step:6.5221808124291e-05 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
21
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Curled New
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)+z*sqr(x(z))+x.i Params NMax:100 Eps:0.0021 [x(0) "z"] "Constant c" Re:-20 Im:0 Use fast algorithm[√] Region Center X:-0.657031953125 Center Y:-0.007414609375000 Step:0.0014359356689453 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data"Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
22
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang
[ ]Use precompile functions... (Vivid 02 Color Palette) f(z,x)= cos(x)-(cube(x)-√1)/(9*sqrt(x)) Params NMax:100 Eps:0.01 [x(0) "z(P+2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractros [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette"Everything" [√]Show apprach phases
23
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang “X”
[ ]Use precomiled functions... (Vivid 01 Color Palette) f(z,x)= sin(x)-(cube(x)-√006)/(9*sqrt(x)) Params NMax:200 Eps:0.062 [x(0) "z(π+7)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.11733333333333 Center Y:0 Step:0.0021190476190476 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show apprach phases
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FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang “Z”
[ ]Use precompile functions... (Vivid 03 Color Palette) f(z,x)= sin(x)-(cube(x)-√011)/(9*sqrt(x)) Params NMax:200 Eps:0.062 [x(0) "z(π+2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show apprach phases
25
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang Tree
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sin(x)-(cube(x)-√002)/(9*sqrt(x)) Params NMax:100 Eps:0.01 [x(0) "z(π+2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show apprach phases
26
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang Two
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= cos(x)-(cube(x)-√4)/(9*sqrt(x)) Params NMax:100 Eps:0.01 [x(0) "z(π+2)] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractros [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show apprach phases
27
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dang Huh?
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= ƒz(πx-cos(-44.0946))+c*x Params NMax:100 Eps:0.01 [x(0) "z(“ƒ77)"] "Constant c" Re:-2.232325306e-3 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show apprach phases
28
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Deeper Depths
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(cosh(x)+z)e/sinh(x)+c*e.sin(z)-c Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.96285714285714 Center Y:0 Step:0.0005357142857142 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
29
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Depths
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(cosh(x)+z)e/sin(x)+c Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
30
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Discovery One
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= sin(z+x)-i Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-1.74661 Center Y:-0.1310525 Step:0.0002089787946428 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
31
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Discovery
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= cos(z+x(1))-e Params NMax:300 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:11.2221484375 Center Y:0.6724609375 Step:0.0008357456752232 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
32
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Discovery Blue
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sin(z+x(1.2))-sin(Ω2-x) Params NMax:300 Eps:0.021 [x(0) "no data"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:10.82 Center Y:0.47 Step:0.0015848214285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
33
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Discovery Tree
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sin(z+x(1))-i Params NMax:300 Eps:0.021 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:5.808 Center Y:-0.2 Step:0.01 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
34
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Divided Newton
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= x÷(sqr(cube(x))-1)/(3*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show apprach phases
35
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Dragon Detail
[ ]Use precompiled functions... (Forest Color Palette) f(z,x)= sqr(x)+c Params NMax:250 Eps:0.01 [x(0) "z"] "Constant c" Re:-1.26805875 Im:0.04885 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0002321428571428 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
36
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embryo Type
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqr(x)+c Params NMax:400 Eps:0.01 [x(0) "z"] "Constant c" Re:-1.187465903 Im:0.3044442408 Use fast algorithm[√] Region Center X:0.092792538282109 Center Y:0.073902152942345 Step:6.5356444857931e-07 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
37
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Edge Mass
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+z/cos(i-60e)/sqr(x)*sin(779)/abs(z,c) Params NMax:100 Eps:0.1061 [x(0) "z"] "Constant c" Re:-10 Im:0.70970076 Use fast algorithm[√] Region Center X:-0.58 Center Y:-0.552 Step:0.0003571428571428 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
38
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embra
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqr(cos(3.5x))+abs(z.i) Params NMax:200 Eps:0.002 [x(0) "z"] "Constant c" Re:-2 Im:1 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
39
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embrapool
[ ]Use precompile functions... (Vivid 01 Color Palette) f(z,x)= sqr(cos(3.5x))+abs(z.i) Params NMax:500 Eps:0.002 [x(0) "z"] "Constant c" Re:-2 Im:1 Use fast algorithm[√] Region Center X:4.5955454189995e-06 Center Y:0.025980398811691 Step:2.5997213595603e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
40
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embrapool Two
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(sin(∆1.3x)+π(x.i) Params NMax:200 Eps:0.002 [x(0) "z(∆9.5)"] "Constant c" Re:2 Im:-199 Use fast algorithm[√] Region Center X:4.5955454189995e-06 Center Y:0.025980398811691 Step:2.5997213595603e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
41
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embryo
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+c Params NMax:400 Eps:0.01 [x(0) "z"] "Constant c" Re:-1.187465903 Im:0.3044442408 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
42
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embryonyx
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(sin(2x))+abs(z.c) Params NMax:200 Eps:0.002 [x(0) "z"] "Constant c" Re:-1.999 Im:2 Use fast agorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
43
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embry “X” One
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(sin(3x))+abs(x) Params NMax:200 Eps:0.001 [x(0) "z"] "Constant c" Re:-1.999 Im:2 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
44
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embry “X” Tree
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(sin(5x))+abs(x.i) Params NMax:200 Eps:0.002 [x(0) "z"] "Constant c" Re:-1.999 Im:2 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
45
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Embry “X” Two
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(sin(4x))+abs(x) Params NMax:200 Eps:0.001 [x(0) 'z"] "Constant c" Re:-1.999 Im:2 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
46
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Epic C
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= x+(abs(z)-1)/(sqr(x))/cos(πx)+z.z/(2*sqr(3)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
47
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: FD Embryo h.e
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(z*1)+z.i/sqr(i.x)+x Params NMax:300 Eps:0.0011 [x(0) "z(02)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.15053056408447 Center Y:-0.68833120507812 Step:1.0249571881975e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
48
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fine Jewel
[ ]Use precompiled functions... (Embryo Palette Color Palette" f(z,x)= sqr(x(sin(z*100))+cube(X)+z)/sqrt(X,x)xƒ-∂x,c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.072685702707877 Center Y:-4.2048631532631e-0 Step:8.488210421475e-07 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show appraoch phases
49
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Five Arms
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)+z Params NMax:400 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.24437083333333 Center Y:0.71444166666667 Step:1.0114397321429e-05 Use fast algorithm[√] Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
50
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: FracMandel
[ ]Use precomplied functions... (depths Color Palette) f(z,x)= sqr(x)+z*sqr(x)+z/sqr(x)+z Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.75 Center Y:0.0049999999999999 Step:0.0014285714285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
51
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fracpool
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)+ sqr(x)/z/sqr(x)*z.c,i.π+(abs(x)+z)+abs(x)+z*sin(x)*z.c,i.π+(cos(x)+z) Params NMax:100 Eps:0.001 [x(0) "z(sin(z,z(π3)))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region CenterX:-0.75 Center Y:0.0049999999999999 Step:0.0014285714285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
52
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fractal Emblem
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= x+(sin(sin(x))+√300)/(√800*sqr(z)*sin(z)) Params NMax:300 Eps:0.02 [x(0) "√0*sin(i-√0492(e))"] "Constant c" Re:0.00300444 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
53
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fractal Flower
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= x+(sin(c.i*sin(x))+√6)/(√8*sqr(z)*sin(z)) Params NMax:100 Eps:0.002 [x(0)"√c.i*sin(i-√0492(e)"] "Constant c" Re:0.00300444 Im:0 Use fast algorithm[√] Region Center X:0.00010000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
54
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fractal Mask
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x(sin(z*2))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.001 [x(0) "z,ƒinf(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.070312499999995 Center Y:-0.006510416666666 Step:0.0003778366815476 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
55
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fractal Morph
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= cos(sin(x/cos(z))+x/sin(i-60i)/cube(x)/sin(779)-abs(z,c)-cube(sin(x-1678+z-8))) Params NMax:100 Eps:0.00209 [x(0) "z"] "Constant c" Re:-6 Im:-0.1940152 Use fast algorithm[√] Region Center X:-0.58 Center Y:-0.552 Step:0.0003571428571428 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
56
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Fractal Pool
For some unknown reason this project file was lost or mis-placed and I cannot find it... Sorry. I will tell you this with this area for text, and that is the depths achieved in this picture was controled by the Color Palette. You can greatly alter the perception and perspective of a fractal plane utilizing the Color Palette as well as changing the Color Palette settings in the, “Attractors� dialog box area of the program.
57
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: The Gates Of New
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x(sin(z*200))+cube(X)+z)/sqrt(X,x)xƒ-∂c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.070623459339017 Center Y:1.0420976342201e-05 Step:1.0969379621598e-05 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
58
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Golden Cyclop
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqrt(cos(sin(z))+(x)+z)/sqr(x) Params NMax:100 Eps:0.001 [x(0) "zƒ*∂6"] "Constant c" Re:-105 Im:0.3 Use fast algorithm[√] Region Center X:-0.10761904761905 Center Y:-0.003809523809523 Step:0.0015136054421769 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
59
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Great Big New
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(c*x)+zcos(z,e) Params NMax:100 Eps:0.01 [x(0) "z,i"] "Constant c" Re:-1.03 Im:1.460205847e-26 Use fast algorithm[√] Region Center X:0.1 Center Y:0.0039999999999999 Step:0.0020089285714286 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
60
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Heart Mandel
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)+z*sqr(ƒc,ƒe(x))+z/sqrt(sqr(ƒc,ƒe)+z) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
61
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Hub
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= x,i-(sin(z,x)/2)*(2i*sqr(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
62
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Hyperbolic
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= cosh(x)-sqr(x)/2+z*x-sqr(z) Params NMax:250 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.753921875 Center Y:0.678765625 Step:6.1767578125e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
63
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Hyperbolic Julia
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= cosh(x)-sqr(x)/2+c*x-sqr(c) Params NMax:250 Eps:0.01 [x(0) "z"] "Constant c" Re:-0.7406047852 Im:0.6656214844 Use fast algorithm[√] Region Center X:-0.039302884615385 Center Y:0.54801682692308 Step:0.006659673334478 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
64
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Jerry & Mike This fractal was generated by a freind of mine by the name of, Mike. He just happened to come by while I was experimenting and made this fractal from something that I was exploring and we named it after us. [ ]Use precompiled functions... (depths Color Palette) f(z,x)= x-(sqr(cube((x))-1)/(3*sqrt(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
65
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Jeweled Skull
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(cos(cos(z*2))+cube(x)+z/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.43489583333333 Center Y:0 Step:0.0025830950055804 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
66
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Jul Simple
[ ]Use precompiled functions... (Fire Color Palette) f(z,x)= sqr(x)+c Params NMax:500 Eps:0.01 [x(0) "z"] "Constant c" Re:-0.1543540079 Im:1.030468544 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:2.9296875e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
67
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lace One
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= x+(sin(c.i*sin(x))+π6)/(π8*sqr(z)*sin(z)) Params NMax:100 Eps:0.002 [x(0) "πc.e*sin(i-π0(e))"] "Constant c" Re:0.0020444 Im:-9.071845891e-3 Use fast algorithm[√] Region Center X:0.0006000000000003 Center Y:-0.534044444384 Step:0.001117559523683 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
68
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lace Two
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= x+(sin(c.i*sin(x))+π6)/(π8*sqr(z)*sin(z)) Params NMax:100 Eps:0.002 [x(0) "πc.e*sin(i-π0(e))"] "Constant c" Re:0.0020444 Im:-9.071845891e-3 Use fast algorithm[√] Region Center X:0.0006000000000003 Center Y:-0.534044444384 Step:0.001117559523683 Attractors [•] Constant Re:969 Im:00009666 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
69
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Layered New
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+z-sqr(z)+cos(x)-sin(z)/cube(c,x*22) Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
70
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Layered New “Z”
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= sqr(x)+z-sqr(z)+cos(x)-sin(z)/cube(c,x*20i)/inv(c)/sqr(x)/z Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
71
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Leo “Z”
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= sqr(x)-(z)+c Params NMax:850 Eps:0.1 [x(0)"z"] "Constant c" Re:0.78 Im:-0.46 Use fast algorithm[√] Region Center X:0.3828 Center Y:-0.8014 Step:0.0001125 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
72
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lion
Generated from an original with a different Color Palette.
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqr(x)+c Params NMax:300 Eps:0.01 [x(0) "z"] "Constant c" Re:0.39 Im:02 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
73
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lion Cage
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= sqr(x)+i/z+sin(cos(x)) Params NMax:500 Eps:0.031 [x(0) "z"] "Constant c" Re:-1.39 Im:8.935343023e-24 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
74
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lion Chain
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqr(ßx.i)-c Params NMax:300 Eps:0.01 [x(0) "z.i*1.5"] "Constant c" Re:-1.39 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
75
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lion Tail
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= inv(sin(x))+sqrt(z)+sin(3)-c Params NMax:300 Eps:0.002 [x(0) "z(3)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0023985890652557 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
76
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lion “Z”
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x)-(z)+c Params NMax:300 Eps:0.01 [x(0) "z"] "Constant c" Re:0.34 Im:-0.2 Use fast algorthm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
77
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Lost Mandelbrot
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= sqr(x)+z Params NMax:2000 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.075120251939548 Center Y:0.65985819973322 Step:2.8658396413957e-10 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
78
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Magnetic
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr((sqr(x)+z-1)/(2*x+z-2)) Params NMax:100 Eps:0.01 [x(0) "0"] "Constant c" Re:0 Im;0 Use fast algorithm[√] Region Center X:1.2846153846154 Center Y:0 Step:0.004429945054945 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Blue" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
79
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Magnetic Two
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr((cube(x)+3*(z-1)(z-2))/(3sqr(x)+3(z-2)x+sqr(z)-3z+3)) Params NMax:100 Eps:0.01 [x(0) "0"] "Constnat c" Re:0 Im:0 Use fast algoritm[√] Region Center X:1.0307692307692 Center Y:0.034615384615385 Step:0.0029876373626374 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Green" [ ]Show approach phases
80
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Maple Leaf
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= cos(x+e*z)sqrt(cos(z+3)) Params NMax:300 Eps:0.001 [x(0) "0"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.2189037037037 Center Y:0.024681481481481 Step:2.6984126984127e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
81
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Maple Leaf Two
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= cos(x+e*z)sqrt(cos(z*.30)) Params NMax:300 Eps:0.001 [x(0) "0"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.21795925925926 Center Y:0.032668783068783 Step:3.3248299319728e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
82
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Massive Mandel
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(x)+z*sqr(x)+z/sqr(x)+z Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
83
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Mass Mandel
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(x)+z*sqr(ƒc(x))+z/sqrt(sqr(x)+z) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
84
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Mirrored Masks
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= sqr(x(sin(z*200))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.069667778678307 Center Y:-1.2225484812067e-0 Step:2.7175753385121e-05 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
85
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: ModiCos
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= x-(cos(cube(x))-√1)/(√3*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "√z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
86
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Modified Newton
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= x-(sqr(cube(x))-1)/(3*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
87
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: ModiSin
[ ]Use precompiled functions... (mesa Color Palette) f(z,x)= x-(sin(cube(x))-√1)/(√2*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "√z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
88
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: ModiSin Cube
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x-(sin(cube(x))-√2)/(√60*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "√z*cube(i)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
89
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Modified Sin Cube Two
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= x-(sin(cube(x))-√5)/(√9*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "√z*cube(i)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
90
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: My Two Cents
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr((cube(1(z)+x-1))) Params NMax:100 Eps:0.301 [x(0) "z(sqrt(.001))"] "Constant c" Re:0.2915 Im:-7.97286625 Use fast algorithm[√] Region Center X:0.1263041015625 Center Y:-0.004798828124999 Step:0.0002469451904296 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
91
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Neon Phareo
[ ]Use precompiled functions... (Palatte Color Palette) f(z,x)= sqr(x(sin(z*100))+cube(X)+z)/sqrt(X,x)xƒ-∂x,c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(,2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.072685702707877 Center Y:-4.2048631532631e-0 Step:8.488210421475e-07 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
92
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Again
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x(x))+e Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.004 Center Y:0 Step:0.0020535714285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
93
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Again “A”
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(x(z))+x.i Params NMax:100 Eps:0.0208 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0311944127269222 Center Y:0.11808859912978 Step:0.0032439523890937 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
94
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Edge
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqrt(x)+zˆcos(x*i)c.e Params NMax:400 Eps:0.0021 [x(0) "z"] "Constant c" Re:-2.000976 Im:2 Use fast algorithm[√] Region Center X:-0.004 Center Y:0.008 Step:0.0007142857142857 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
95
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Edges
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqrt(x)+zˆπ(z*i)c.e+exp(x) Params NMax:400 Eps:0.002 [x(0) "z(9)"] "Constant c" Re:0 Im:9 Use fast algorithm[√] Region Center X:-0.004 Center Y:0.008 Step:0.0007142857142857 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
96
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Foreground
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sin(e)+z*sqr(x)÷c.e Params NMax:300 Eps:0.001 [x(0) "z(001)"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.1759125078125 Center Y:0.54043337890625 Step:6.2966927664621e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
97
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New New
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= sqr(z*x)+z Params NMax:300 Eps:0.0022 [x(0) "z"] "Constant c" Re:-1.000098365 Im:900 Use fast algorithm[√] Region Center X:-0.065514285714286 Center Y:0.018551428571429 Step:0.003297193877551 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
98
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Opening
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+z,i-39e/sqr(x)+z,i-39e(sin(sqr(x)+z,i39e))+(cos(sqr(x)+z,i-39e))*2c Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.002 Center Y:0.203 Step:0.0011272321428571 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
99
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Newton
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x-(cube(x)-1)/(3*sqr(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0028571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Everything" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show approach phases
100
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Tree
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sin(e)+z*sqr(x)-c.i Params NMax:300 Eps:0.01 [x(0) "z(1)"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.4502225 Center Y:0.58420625 Step:0.0004090931919642 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
101
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Two
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sin(e)+z*sqr(x)-c.i Params NMax:300 Eps:0.01 [x(0) "z(1)"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.565 Center Y:0.649 Step:8.2589285714286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
102
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: None
[ ]Use precompiled functions... (Rainbow Color Palette) f(z,x)= i*=2c/23(z+x) Params NMax:400 Eps:0.04 [x(0) "z"] "Constant c" Re:1.00067432 Im:1.00067432 Use fast algorithm[√] Region Center X:0 Center Y:-0.00844444444440 Step:0.0014231150793576 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show approach phases
103
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: None Tree
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= i*=2c/23(z+x) Params NMax:400 Eps:0.04 [x(0) "z"] "Constant c" Re:-1.00067432 Im:0.04 Use fast algorithm[√] Region Center X:0.0026564814814675 Center Y:-0.003131481481465 Step:9.7246197089437e-05 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show approach phases
104
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: None Tree X
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= i*=2c/23(z+x) Params NMax:400 Eps:0.04 [x(0) "z"] "Constant c" Re:-1.00067432 Im:0.04 Use fast algorithm[√] Region Center X:0.0026564814814675 Center Y:-0.003131481481465 Step:9.7246197089437e-05 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
105
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: None Tree Z
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= i*=1c/29(z+x) Params NMax:100 Eps:0.034 [x(0) "z"] "Constant c" Re:6.00067432 Im:0.034 Use fast algorithm[√] Region Center X:0.0026564814814675 Center Y:-0.003131481481465 Step:9.7246197089437e-05 Attractors [•] Constant Re:6.00097654 Im:-1.0098000456 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
106
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: None Two
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= i*=2c/23(z+x) Params NMax:400 Eps:0.04 [x(0) "z"] "Constant c" Re:-1.00067432 Im:0.04 Use fast algorithm[√] Region Center X:-/--26564814814675 Center Y:-0.003131481481465 Step:0.0009724619708943 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [ ]Consider as attractor/Palette:"Everything" [√]Show approach phases
107
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: New Wicked
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqrt(x*-8)/+z*(x) Params NMax:100 Eps:0.002 [x(0) "z"] :"Constant c" Re:24.7543 Im:1.3243e-05 Use fast algorithm[√] Region CenterX:0.0039653846153849 Center Y:0 Step:0.0047724931318681 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
108
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Oriental Mozaik
[ ]Use precompiled functions... (depths Color Palette) f(z,x)= sqr((sqr(x)+c-1)/(2*x+c-2)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:1.2915 Im:0.97286625 Use fast algorithm[√] Region Center X:-0.405 Center Y:0.4725 Step:0.0084375 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
109
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Overview
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x(sin(z*200))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.071320064484122 Center Y:-0.000968812003968 Step:6.5221808124291e-05 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
110
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Palette X
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+z+sqr(x)+z*300z,z/x,e Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.005190217932876 Center Y:0.0002417552714446 Step:0.0002156163096080 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
111
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Palette Text
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+z+sqrt(x)+z*900z,z/x,e-(sin(z.e-X))/cube(cos(x)) Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.004999999999999 Center Y:1.1102230246252e-16 Step:0.0002176339285714 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
112
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Pattern Swirl
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqrt(x+i)*sqr(z(x/z))+z.i Params NMax:400 Eps:0.0001 [x(0) "z"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.93180731947763 Center Y:0.048743044362749 Step:9.1925810490336e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
113
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Pattern Swirl
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqrt(x+i)*sqr(z(x/z))+z.i Params NMax:200 Eps:0.0022 [x(0) "z"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.92856950683594 Center Y:0.047856372070312 Step:7.4907302856445e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
114
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Point Of Change
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr9x)+z*sqrt(ƒx,ƒe(x))+z/sqrt(sqr(ƒx,ƒe)+z)+sqr(x)+z*sqr(ƒx.i,ƒe(x.i))+z/sqrt(sqr(ƒx,ƒe)) Params NMax:100 Eps:0.071 [x(0) "z"] Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.060294363839286 Center Y:-2.0926339285714e-0 Step:8.2744453808309e-06 Attractors [•] Constant Re:-1.0 Im:0 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
115
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Prisim
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x+(sin(c.i*sin(x))+π6)/(π8*sqr(z)*sin(z)) Params NMax:100 Eps:0.0002 [x(0) "√5c.e*sin(i-π0(e))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0006000000000003 Center Y:-0.51666018512671 Step:0.0016142526453199 Attractors [•] Constant Re:969 Im:00009666 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
116
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Qoul
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= c*(x)+z(sqr(cos(x)))/sqrt(z) Params NMax:100 Eps:0.0015 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.54210526315789 Center Y:0.0042105263157894 Step:0.0039473684210526 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
117
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Rainbow
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x-(inv(z)+2)/(20*sqr(i)) Params NMax:100 Eps:0.021 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.452 Center Y:0.008 Step:0.0036607142857143 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
118
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Rainbow C
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(z(sqr(z)+x))+x(cos(z)+c) Params NMax:300 Eps:0.0022 [x(0) "z"] "Constant c" Re:-1.908746 Im:0.3 Use fast algorithm[√] Region Center X:-0.62407467532468 Center Y:0.0056980519480519 Step:0.0010897096764842 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
119
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Rain Zone
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(z(sqr(z)+x))x(cos(z)+c) Params NMax:400 Eps:0.0022 [x(0) "z"] "Constant c" Re:-1.908746 Im:0.3 Use fast algorithm[√] Region Center X:-0.4718448126366 Center Y:0.40126978444096 Step:0.0008587595273288 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
120
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Red Bryonyx
[ ]Use precompiled functions... (Embryo Palete Color Palette) f(z,x)= sqr(cos(.5x))+abs(z.c) Params NMax:200 Eps:0.002 [x(0) "z"] "Constant c" Re:-2.999 Im:2 Use fast algorythm[√] Region Center X:0.010626483288972 Center Y:0.015331402249547 Step:3.6194396514568e-07 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
121
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Red Star
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= x-(sin(cube(x))-√80)/(√60*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "√z*cube(e)"] "Constant c" Re:0 Im:0 Use fast agorithm[√] Region Center X:0.00010000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
122
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Red Tile
[ ]Use precompiled functions... (Vivid 03 Color Palette) f(z,x)= sqrt(x*.000009)+i Params NMax:200 Eps:0.01 [x(0) "z*x*+8i"] "Constant c" Re:-1 Im:0 Use fast algorithm[√] Region Center X:-0.032 Center Y:-0.0992 Step:0.0003946428571428 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
123
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Royal Crest
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x-(sin(sin(x))-√31000)/(√50000*sqrt(x)*cos(x)) Params NMax:100 Eps:0.031 [x(0) "√z*sin(e+√1(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
124
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: The Same As
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= c*(x/x-.100+i)+z(sqr(cos(x)))-.03z+sin(π-sqrt(z))cube(c/.200) Params NMax:100 Eps:0.001 [x(0) "z/sin(πz-33)"] Use fast algorithm[√] Region NMax:100 Eps:0.001 [x(0) "z/sin(πz-33)"] "Constant c" Re:0 Im:0 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
125
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Shell
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+c Params NMax:2000 Eps:0.01 [x(0) "z"] "Constant c" Re:-1.674364692 Im:0.005736695645 Region Center X:-5e-05 Center Y:5e-05 Step:9.7098214285714e-06 Use fast algorithm[√] Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
126
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Sibling Embryo
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqrt(z)+c(sin(x*2(sqr(e,x)))) Params NMax:200 Eps:0.001 [x(0) "z(1πc,e)"] "Constant c" Re:-3 Im:0 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
127
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Side Plane
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(cos(.05x))+abs(z.c)*sqr(abs(.02x)) Params NMax:200 Eps:0.002 [x(0) "z/c,i"] "Constant c" Re:-1.999 Im:-4 Use fast algorithm[√] Region Center X:0.010626483288972 Center Y:0.015331402249547 Step:3.6194396514568e-07 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
128
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: “Sine
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= c*sin(x) Params NMax:1 Eps:0.4 [x(0) "z"] "Constant c" Re:1 Im:04 Use fast algorithm[√] Region Center X:0 Center Y:0 Step:0.0075353218210361 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
129
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Smoke
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+z Params NMax:2000 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.075299233398438 Center Y:0.66007116943359 Step:1.0202080862863e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
130
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spectro
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x+(sin(sin(x))+√300)/(√2000*sqrt(z)*cos(z)) Params NMax:100 Eps:0.004 [x(0) "√0*sin(i-√02(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
131
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spectro “X”
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x+(sin(sin(x))+√300)/(√2000*sqrt(z)*cos(z)) Params NMax:100 Eps:0.004 [x(0) "√0*cos(i-√02(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
132
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spectro “Z”
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x+(sin(sin(x))+√300)/(√2000*sqrt(z)*cos(z)) Params NMax:100 Eps:0.004 [x(0) "√0*sin(i-√02(i))"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.00234375 Attractors [•] Constant Re:5 Im:0 Expr:"no data" Palette:"Re" Infinity [√]Consider as attractor/Palette:"Everything" [√]Show approach phases
133
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spiral
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+c Params NMax:765 Eps:0.001 [x(0) "z"] "Constant c" Re:-0.99 Im:0.2 Use fast algorithm[√] Region Center X:0.0002714277727142 Center Y:0.020614748024143 Step:0.0038372508769133 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
134
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spiral “X”
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+c Params NMax:495 Eps:0.07 [x(0) "z"] "Constant c" Re:-0.030099 Im:0.74856433 Use fast algorithm[√] Region Center X:0.004987594864551 Center Y:0.019575175320061 Step:0.0035023004737609 Attractors [•] Constant Re:-.2003672109 Im:0.00034567e Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
135
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Spiral “Z”
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(x)+c Params NMax:495 Eps:0.07 [x(0) "z"] "Constant c" Re:-0.030099 Im:0.74856433 Use fast algorithm[√] Region Center X:-0.023934599013 Center Y:0.039993542667 Step:0.0036428571428571 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
136
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Split Newton
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= z-(sqr(cube(c))+1)/(3*sqr(x)*cube(i)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:-0.18214285714286 Step:0.0035993303571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
137
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Star
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(cosh(x)+sin(x)+c)*sqr((cube(x)+3(c-1)x+(c-1)(c-2))/(sqr(x)+3(c-2)x+3c+3)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.70285714285714 Center Y:0 Step:0.0027393100097182 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
138
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Stretched Embryo
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= sqr(x)+c-1.00456e/sqr(x)+abs(z) Params NMax:400 Eps:0.003 [x(0) "z"] "Constant c" Re:-1.18333333 Im:0.3011442408 Use fast algorithm[√] Region Center X:0.008157321729 Center Y:0.020638957519 Step:2.8686580519286e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
139
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Stretched Embryo h
[ ]Use precompiled functions... (Rainbow Color Palette) f(z,x)= sqr(x)+c-1.004e/sqrt(x)+sin(z)/sqr(x)*abs(x) Params NMax:400 Eps:0.053 [x(0) "z"] "Constant c" Re:-0.88333333 Im:0.3011442408 Use fast algorithm[√] Region Center X:0.021481431570131 Center Y:0.016094967306519 Step:6.6444171558244e-06 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
140
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Symetric C
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x+(sqr(abs(∂0.9))+cos(0.5))/(x.i*cube(e.i)*abs(z)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
141
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Symetric Circle
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x÷(sqr(cube(x))-3)/(2*sqr(x)*cube(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:0.016171428571429 Center Y:-0.016071428571429 Step:0.0059191645408163 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
142
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Symetric Circles
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x-(sqr(abs(∂0.1))+cos(0.5))/(x*cube(e.i)*abs(z)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:o.0001000000000002 Center Y:0 Step:0.0053571428571429 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Re" Infinity [ ]Consider as attractor/Palette:"Everything" [ ]Show approach phases
143
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Taj Mahal
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sqr(c*x)+z*cos(z,e) Params NMax:100 Eps:0.001 [x(0) "z,i/3"] "Constant c" Re:-1.03 Im:-1.03 Use fast algorithm[√] Region Center X:0.0020371093750001 Center Y:0.0417138671875 Step:0.0019084036690848 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases Taj Mahal 144
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: The Jaws
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(x(sin(z*20))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.077842245296551 Center Y:-0.000316593922725 Step:7.279219656729e-05 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases The Jaws 145
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: TriSpheres
[ ]Use precompiled functions... (Vivid 01 Color Palette) f(z,x)= x-(sin(x)-2)/(2i*sqr(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.5 Center Y:0 Step:0.0028571428571429 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
146
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Vertical Horizen
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= x,i-(sin(z,x)/09)*(2i*sqr(x))x/(cube(x)) Params NMax:100 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-1.1095238095238 Center Y:-0.083809523809524 Step:0.0031377551020408 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
147
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: VeryCos
[ ]Use precompiled functions... (Palette Color Palette) f(z,x)= sin(z+x)-i Params NMax:200 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-1.7144028320313 Center Y:-0.17202734375 Step:0.0002864783150809 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
148
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Volcano
[ ]Use precompiled functions... (Fire Color Palette) f(z,x)= inv(sqr(x)+1)-sqr(x)+z Params NMax:250 Eps:0.01 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.2314794983838 Center Y:0.049136864512426 Step:2.0646136882453e-05 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
149
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: World Point
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= (z/x+i)+z(sqr(cos(x)))-.0z+sin(π-sqr(e.i))sin(c) Params NMax:100 Eps:0.0301 [x(0) "z/abs(πz*13)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.031593911577333 Center Y:-0.010693947797992 Step:0.0013584588575667 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
150
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Journal 1999 ~ 2001
J. Baker CP Studio
Title: Worm
An original “Worm” with a different Color Palette.
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr((sqr(x)+c-1)/(2*x+c-2)) Params NMax:250 Eps:0.01 [x(0) "z"] "Constant c" Re:3.006984536 Im:0.5194957116 Use fast algorithm[√] Region Center X:-2.014822265625 Center Y:-0.5029171875 Step:0.0003960845947265 Attractors [•] Constant Re:1 Im:0 Expr:"no data" Palette:"Red" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
151
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Yellow Tip
[ ]Use precompiled functions... (Embyro Palette Color Palette) f(z,x)= sqr(x)+z*sqr(x(z,x))+x Params NMax:100 Eps:0.0021 [x(0) "z"] "Constant c" Re:-20 Im:0 Use fast algorithm[√] Region Center X:-0.904609375 Center Y:-0.33233984375 Step:0.0002748413085937 Attractors [ ] Constant Re:"no data" Im:"no data" Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
152
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio
Title: Zipper
[ ]Use precompiled functions... (Vivid 02 Color Palette) f(z,x)= sqr(cos(cos(z*2))+(x)+z)/sqrt(e)xƒ-∂1c Params NMax:100 Eps:0.001 [x(0) "z"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:1.390625 Center Y:0 Step:0.042724609375 Attractors [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases
153
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H Editors Statement January 7th, 2002
I also want to thank, Adobe Systems Software!
First of all I want to extend a thank you to, Martin Hairer for allowing me to use the, User Manual and Read Me’s associated with, FractalDesigner and, Amadeus II so that the fractals provided herein have a formal document to fall back onto for proper reference. I want to also add that I am by no means a mathematician and the formulas that are supplied with each fractal are only my experimentations with the program. I have in fact broken a couple of rules if you read the manual closely and some of the operators used are not listed in the User Manual and are not recommended so if you see some redundant use of characters or math formulas that are totally incorrect that is why. If you can generate the same exact results utilizing correct math then please by all means do so and forward it on to me rather than, Martin since he does do his math correctly and I am sure doesn’t want to be bothered with that. Of course, any pertinent questions regarding the software and its performance should be directed to him at his respective email address noted in places throughout this PDF Journal. Once you have read the Manual a couple of times and see exactly what, Martin is trying to point to all of us as users you will see by example the instances where I have broken the rules and by doing so be able to see by that example what it is that he tries to point out in his description of how the program works and also how to compile an algorithm. FractalDesigner is one of the first software programs that I bought online for my Mac G3/233 in, 1999 and has since that time been one of my favorite software’s to play with and exercise discovery in only a way that a Mac can do it. I have used FractalDesigner fractals in a lot of other things other than just my web gallery too, I have used them along with, Strata Studio Pro 2.1.1 in a compilation of a collection of digital/audio synthesist artist’s from all over the world on a CD set named, “Metasynthia Project 1” on disc “A” for animation graphics whereas I utilized FractalDesigner’s fractals as texture maps in the animation scene that I made for the, U&I Software Company that was doing the CD Collection as a promotional effort for their flagship products. 154
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I Editors Statement continued... The CD’s can be obtained from the, U&I Software web site at: http://www.uisoftware.com Another example of the use of the, FractalDesigner fractal software was my submittal of fractal textures for use in a 3D software’s texture library which actually happened first before the CD contribution and as far as I know is the first set of texture examples of their type. That was for the, Pixels Animation Studios, Pixels 3D Studio software shaders. Since then I have uploaded a number of other shader texture examples using FractalDesigner fractals to the, StrataCafe and that software’s version of shader textures located in that repository of user items of all sorts. So far... The only other Macintosh PowerPC software that I have and or have seen or used that even comes close to, FractalDesigner is, U&I Software’s “ArtMatic Pro 4” since, Eric Wenger utilizes the, Mandelbrot and Julia Sets within that software algorithm but it still is not even close to the same thing keeping, FractalDesigner a very unique and original fractal generator even though, FractalDesigner isn’t nearly as complex of a software by comparison. I want to continue to record the time that I spend with, FractalDesigner as time passes and maybe even improve on my math in formulas as well as improvements in this media format. I would really like to see a small forum of, FractalDesigner users pulled together eventually so that there are more and more people that can get information regarding this incredible software. I have made requests at various times both at my main web site at Tripod and in e-mail for other users of the, FractalDesigner software so as to hopefully start building the collection of known users with the intention of learning more with others how to control and manipulate the fractal algorithm and in doing so gain a deeper knowledge of fractals and how they work. I have watched a couple of PBS television programs that explain the fractal in a much broader sense and claim that fractal geometry is everywhere in life, from the shapes of natural things like trees or clouds to rocks and molecules that are in everything within and around all of us all the time. Besides the most obvious reasons that I spend time at a computer generating fractal art is because they are so interestingly beautiful and a blind curiosity regarding fractals and the math that represents them. 155
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I Editors Statement continued... If you are like me, in that math has never been one of the hottest subjects to ever cross your learning path but at the same time have always had a sence of understanding about what that’s all about then you will more than likely get a better gist for what I have provided with this PDF document in as far as what is there (Art) and what it is representative of. I am a person/artist that has always understood more than I really know technically speaking that is but am gaining a deeper knowledge by using the computer and some of the technological software that are available today for the Mac and therefore am beginning to see these type of things from a different stand-point-of-view; kind of like buying a software and using it for quite a while before ever reading anything but the contents in the User Manual. Now as I casually learn more and more regarding fractal math and geometry I have a clearer understanding as to how they work and how it all could play a larger part in the worlds around us everyday. If I were to have read the technical aspects of the manual I would have been way confused and not really correlated the programs abilities mathematically or procedurally or even from a color aspect which plays a strong role in the appearance of a lot of fractals generated with FractalDesigner. Color, is the second most powerful tool to utilize with FractalDesigner to generate variations of individual fractal formulas expanding the possibilities that it has the potential to produce. From an artist’s stand-point-of-view fractal art is always popular by a wide range of age groups, especially when they find out that it wasn’t created with tie-die and that a math formula was utilized to make it and so everything about it is gratifying and a never-ending discovery.
Contact Information to the Author. Jerry Baker (Coloredpencilguy)
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A short explanation of how to reproduce the fractals in this PDF. I would start out by entering data in the, “Functions...” dialog box and then go to the, “Region...” dialog box and enter data there then to the, “Attractors...” dialog box and enter data there third. Last of all since it is a user preference anyway the, “Color Palette...” dialog box and either try and duplicate the colors that I had in the palettes used in the samples located at the beginning of this journal or of course create your own.
[ ]Use precompiled functions... (Embryo Palette Color Palette) f(z,x)= sqr(x(sin(z*20))+cube(x)+z)/sqrt(X)xƒ-∂c Params NMax:100 Eps:0.0021 [x(0) "z,ƒinv(.2)"] "Constant c" Re:0 Im:0 Use fast algorithm[√] Region Center X:-0.077842245296551 Center Y:-0.000316593922725 Step:7.279219656729e-05 There are square brackets in the text to show a button Attractors style selection or for a checkmark selection. [•] Constant Re:-1.0 Im:3 Expr:"no data" Palette:"Everything" They have an “Option 8” marking or a checkmark or none. Everything else is fairly obvious as to what goes where. Infinity [√]Consider as attractor/Palette:"Everything" [ ]Show approach phases 157
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Information about, Amadeus II. Also by, Martin Hairer.
Amadeus II v3.2.2 June 25, 2001 Amadeus II is a powerful tool that allows you to process, generate and analyze sounds. Unlike other programs of the same type, Amadeus II is fast (even when handling large files direct-to-disk), it supports Mp3 encoding, and it offers several file repairing functions. Finally, Amadeus II provides the experienced user with a lot of analyzing functions, real-time or not. There is no need for a special installation of Amadeus. Simply click on the icon “Amadeus II” to open the program. Amadeus II is not a freeware. If you decide to keep it and want to be able to save your files, please pay the shareware fee of 25$. Thank you very much! You will find detailed information about registering in the “Register” folder. The easiest way of registering is online at <http://order.kagi.com/?L85>. This version works on any Power Macintosh with MacOS 8.6 or later and 10MB free RAM. It also requires CarbonLib to be installed. It is a PowerMac binary, so it will not work on 68k machines. QuickTime 4.1 is required in order to access to all functions. If you want to contact the author, please send an E-Mail to: Martin.Hairer@math.unige.ch 158
Continued on the next page.
FractalDesigner 2.01
Journal 1999 ~ 2001
J. Baker CP Studio You can also write to: Martin Hairer 19, ch. des Cyprès CH-1226 Thônex Switzerland
The history list here only reflects the current status of the product as it is today, more information can be obtained from, Martin’s web site. Use the hyperlink URL below to go directly to the site and read more on the history.
or visit my homepage at http://www.unige.ch/math/folks/hairer/martin
A french version of Amadeus II is also available on that page. If you find any bugs or have suggestions to improve this program, I’ll be happy if you contact me. Here is a short history of the major improvements made to the different versions: Amadeus II v3.2.1 & v3.2.2 - Bug fixes of version 3.2. Amadeus II v3.2 - New user interface. - Runs on MacOS X. - New de-noising function. - Support of variable bitrate Mp3 encoding. - Support of the new Ogg Vorbis file encoding format. - Exporting of markers as cue points in WAVE and AIFF files. - Support of the SoundDesigner II file format. - New stereo utilities.
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I want to say that this application is one of the most useful sound editing applications I have in my collection. Also it is fully functional in OSX which is an added plus for those that have editing demands in that operating environment. When I want to detail any sound with certain control over what and why I use Amadeus and recommend it to any Synthesist or digital musician working with today’s audio and audio/graphics software.
FractalDesigner 2.01 User Manual and
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Contents
Main Contents
• The FractalDesigner User Manual • The Amadeus II Information page
• The Lyapunov Fractal ReadMe • The Editors Statement
• Color Management
• Attractors
• Designing your own Algorithms
• Basic Manipulations
• The Algorithms
• The Interpreter
• Registering
• Julia and Mandelbrot Sets
• Special Behaviors
I want to again state that the fractals and formulas that I have published in this book journal are meant merely for the purpose of documenting and publishing the three years that I have used FractalDesigner up to this point and are only for starting points only. They and the formulas are only skimming the surface in most instances and can be taken way deeper by utilizing the, “Attractors...” dialog box and “Region...” dialog box. Any questions regarding the settings and or formulas given can be directed to me, Jerry Baker at, jbakerstudio@earthlink.net
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Read Meâ&#x20AC;&#x2122;s FractalDesigner v2.01 FractalDesigner is a very powerful tool that allows you to create fractal images based on the convergence of iterations of the type x_0 = f(c,z) x_(n+1) = g(x_n,z,c) where c is a fixed constant and z is the location in the complex plane. The most known examples of such fractals are the Mandelbrot set (f(c,z) = 0 and g(x,z,c) = x^2 + z) and Julia sets (f(c,z) = z and g(x,z,c) = x^2 + c). With FractalDesigner, it is possible to reproduce those pictures but also to explore various other functions thanks to the integrated interpreter. In order to gain speed, it is also possible to compile an algorithm and to call it from the program. This program is not a freeware. If you decide to keep it and want to be able to save your files, send me 20$ in order to get your personal registration code (see the paragraph â&#x20AC;&#x153;Registering FractalDesigner belowâ&#x20AC;?). Thank you very much! This version works on any PowerMacintosh with System 7.6 or later, including MacOS 8 and 8.1. It is a PowerPC application, so it will not work on 68k based machines. If you want to contact me, send an E-Mail to: hairer@kagi.com Martin.Hairer@erehwon.org Martin.Hairer@math.unige.ch 161
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Read Me’s You can also write to: Département de Physique Théorique 24, Ernest Ansermet CH-1211 Genève 4 Switzerland
Homepage: http://mpej.unige.ch/~hairer/ EMail: Martin.Hairer@math.unige.ch Tel.: ++41 22 702 63 84 or visit my homepage at
http://www.erehwon.org/hairer/ or http://www.unige.ch/math/folks/hairer/martin On this homepage, you’ll always find the latest version of the program. If something doesn’t work or works wrong, or if you simply have suggestions to improve this program, I’ll also be happy if you’d contact me. Registering FractalDesigner FractalDesigner has the following pricing: 1- 10 single user licenses, $20 per user 11+ single user licenses, $15 per user A Site License costs $350 (roughly equal to 27 users) and covers all locations for your organization within a 160 kilometer radius of your site (100 miles). One big advantage of a Site License is that you do not need to keep track of how many people at your site are using the software. A World-Wide License costs $1400 and it covers all locations for your organization on the earth. 162
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Read Meâ&#x20AC;&#x2122;s Paying for FractalDesigner is fairly simple. Open the Register program that accompanies FractalDesigner. Enter your name, your email (or/and postal) address, and the number of single user licenses you desire for each program you wish to purchase (or Site or World-Wide licenses). Save, Copy or Print the data from the Register program and send the data and payment to Kagi. Kagi handles my payment processing. If you pay with Credit Card or First Virtual, you can email or fax the data to Kagi. Their email address is sales@kagi.com and their fax number is +1 510 652-6589. You can either Copy the data from Register and paste into the body of an email message or you can Save the data to a file and you can attach that file to an email message. There is no need to compress the data file, itâ&#x20AC;&#x2122;s already pretty small. If you have a fax modem, just Print the data to the Kagi fax number. Payments sent via email are processed within 3 to 4 days. You will receive an email acknowledgment when it is processed. Payments sent via fax take up to 10 days and if you provide a correct internet email address you will receive an email acknowledgment. If you are paying with Cash or USD Check you should print the data using the Register application and send it to the address shown on the form, which is: Kagi 1442-A Walnut Street #392-L85F Berkeley, California 94709-1405 USA
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Read Me’s You can pay with a wide variety of cash from different countries but at present if you pay via check, it must be a check drawn in US Dollars. Kagi cannot accept checks in other currencies, the conversion rate for non-USD checks is around USD 15 per check and that is just not practical. If you have a purchasing department, you can enter all the data into the Register program and then select Invoice as your payment method. Print three copies of the form and send it to your accounts payable people. You might want to highlight the line that mentions that they must include a copy of the form with their payment. Kagi can not invoice your company, you need to act on my behalf and generate the invoice and handle all the paperwork on your end. Please do not fax or email payment forms that indicate Cash, Check or Invoice as the payment method. As far as we know, there is still no technology to transfer physical objects via fax or email and without the payment, the form cannot be processed. Payments send via postal mail take time to reach Kagi and then up to 10 days for processing. Again, if you include a correct email address, you will hear from Kagi when the form is processed. Protection FractalDesigner has a protection scheme and when you pay, Kagi give you a registration code in order to indicate to FractalDesigner that you have paid the registration fee. If you do not have an email address, please enter your complete postal address and please remember, they do not know what country you live in so please enter that into the postal address also. If you do not have an email address you should consider selecting the Postcard Receipt so that Kagi can inform you of your registration code. Kagi transmits the registration codes via email and paid postcard receipt only. You’ll have to select the menu item “Register...” ,in the apple menu to give the program your registration code. This will unlock the saving and printing functions. History Here is a short history of improvising made to the different versions: FractalDesigner 1.0 First beta version. 164
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Read Me’s FractalDesigner 1.1 First released version. The main ameliorations compared to version 1.0 concern the interface (possibility to open several dialogs at the same time, higher conformance to Apple programming standards). It is also possible to save a color palette and to copy the picture.
FractalDesigner 2.01 - Some bugs concerning the management of precompiled functions are fixed. - Lyapunov toolkit is available.
FractalDesigner 1.2ß The size of the window is now independent of the size of the picture. There is a “full screen” function that allows to use the whole screen including the menu bar to show the picture. If the picture is bigger than the screen, you can move it using the arrows. This version is a beta version, so it has not been fully tested. If there remain some bugs, please tell me. FractalDesigner 1.21 A few minor bugs concerning mainly the display have been corrected. The pictures can be saved as PICT files. They can be viewed and printed at different resolutions. FractalDesigner 2.0 - The user interface has been entirely rewritten and uses now the objects of Amadeus II. - The location of the attractors can depend on c and z. - The management of colors is entirely rewritten. - Pictures can be exported in any of the formats your version of QuickTime supports. - The colors of the pictures can be animated with the help of a slider.
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Lyapunov Fractals This package allows you to generate so-called Markus-Lyapunov type fractals. It requires FractalDesigner v2.01 or later, which can be downloaded from http://www.erehwon.org/hairer/ One possibility is to open one of the examples with FractalDesigner and to explore the pictures. Another possibility is to create a new document with FractalDesigner and to check the “Use Precompiled Function...” flag in the “Function” dialog box. Then choose one of the two Algorithm files included with this package. Have fun! Martin Hairer
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E
Introduction
Thank you for using FractalDesigner. This toy/tool will allow you to explore the beautiful world of fractal images and to design your own pictures. Unlike many similar products, FractalDesigner allows you to change the algorithm used to compute the picture, leaving virtually every possibility open to reveal the beauty hidden at the edge of chaos. I do not represent any software company or whatsoever. I am just a graduate student in physics who likes programming. This program was developed entirely during my free time and is not part of any bigger project. Because of these reasons, no exhaustive testing could have been performed. Since some functionalities are system-dependant or even machine-dependant, it may happen that FractalDesigner presents some dysfunctionalities on your personal configuration. If so, please feel free to contact me at: Martin.Hairer@math.unige.ch Just to avoid getting into trouble, I have to mention that I am not responsible for any damage that may be caused by FractalDesigner to your machine. You can always download the latest version of FractalDesigner from my homepage at: http://www.erehwon.org/hairer/ OR http://www.unige.ch/math/folks/hairer/martin/ There are always a new and extensive collection of FractalDesigner renders online in one of two internet locations hosted by Coloredpencilguy, thru Tripod.com and at, iTools at: http://coloredpencilguy.tripod.com/jbstudio/page-01.html
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First Steps
Installation Just copy the content of the folder FractalDesigner v2.0 onto your hard disc and launch the FractalDesigner application program by double clicking onto it.
E Basic Manipulations When you open FractalDesigner, a window appears and starts to compute the Mandelbrot Set, (for an explaination of what this represents, see next section.). You can select a portion of the picture by clicking into it and dragging the mouse. This selection can then be further modified. If you press the return key, FractalDesigner zooms into the selected zone. You can change the size of the picture with the, “Size...” menu item of the, “Fractals...” menu. You may want to change the colors of the picture by selecting one of the predefined color palettes available in the, “Colors...” menu. The algorithm used by default at the beginning is the, “Mandelbrot” algorithm. If you want to change it, you have to uncheck the, “Use precompiled function...” dialog box. E
The Algorithms The fractals you can draw with FractalDesigner are the basins of attraction of attractors of complex dynamical systems. The screen represents the complex plane. A point of this plane will be denoted by, “z” in the sequel. The algorithm performed by the program is the following.:
= ƒ0(z), xn+1 = ƒ(z,xn), x
0
where, “ƒ” and, “ƒ0 are two functions that can be defined by the user in the, “Function...” dialog box. The algorithm stops when the value, “xn”is loacted at a distance less than, “εε”, (the parameter EPS of the, “Function...” dialog box) of one of the attractors defined by the user in the, “Attractors...” dialog box. Infinity can be defined as an attractor. 168
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Read Me’s In that case, the iteration stops when, “x ” becomes bigger than, “1/εε”. The corresponding point is then colored according to the n color palette linked to the attractor that was reached, (see the Section, “Color Management”). The color corresponds to the number of steps it took to reach the attractor. If no attractor was reached after NMax steps, the corresponding point is colored black. E The Interpreter There is a built-in interpreter in FractalDesigner that is called at each step to evaluate the values of the functions, “ƒ ” and, “ƒ ”. 0 The list of characters recognised by the interpreter are the standard alphanumeric characters, as well as the symbols, (, ), *, + and -. All other characters are simply ignored. The interpreter recognises the basic arithmatic operations. When no operator links two expressions, they are automatically multiplied, (you can write, (x+2) (x-1) instead of, (x+2) (x-1)). The interpreter also recognises the following elementary functions: * Command Meaning
Irt also recognises the constants, “e” and, “i=√−1”. For precise meaning of these functions, see any standard calculus textbook, HW for example [HW HW].
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sin cos tan sinh cosh tanh sqr invert cube sqrt exp log abs
Trigonometric sine Trigonometric cosine Trigonometric tangent Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Square (× ⇒ ×2 ) Inverse (× ⇒ 1//× ) Cube (× ⇒ ×3 ) Square Root (× ⇒ √× ) Expotencial function Natural logarithm Modulus (× ⇒ × )
FractalDesigner 2.01 User Manual and
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Attractors In our case of interest, an attractor is a stable fixed point of the dynamical system. By this I mean a value, “x” such that, ƒ(z,x)=x and the stability condition, ∂xƒ(z,x) <1 holds. This relationship should be valid for every “z”. In the current version of FractalDesigner, the value of the attractors may depend on, “z” and or, “c” (if you choose, “Anal. expr.”) instead of, “Constant”). When, “∞” is chosen as an attractor, the stability condition is replaced by the instability condition, “limx⇒∞∂׃(z,x)>1”. If the stability condition is violated, the corresponding fixed point does not attract neigboring points, and so the corresponding basin of attraction will just be a circle of radius, “εε” which is mearly an artifact coming from our stopping condition.
g
Julia and Mandelbrot Sets The two most famous examples of such algorithms are those that generate the Mandelbrot set and those that generate Julia sets. The Mandelbrot set is generated with the algorithm: x0=0, xn+1=x2n+z The only attractor is, “∞”. The corresponding Julia sets are generated with the algorithm: x0=z, xn+1=x2n+c where, “c” is a user-defined constant. Notice the similarity between both algorithms; we just replaced, “z” by, “c” in the second one. In order to get, “nice” Julia sets, choose the constant, “c” near the boarder of the Mandelbrot set. You can get the coordinate of a point by simply command-clicking on it. You can then copy this location and paste it in the, “Function...” dialog box. In the examples, you’ll find other, “pairs” of algorithms of this kind. For example, the picture, “Magnetic” was generated with: x3+3x(z -1)+(z -1)(z -2)
x0=0, xn+1= 170
3x2+3x(z -2)+(c -1)(c -2)
FractalDesigner 2.01 User Manual and
Read Me’s The picture, “Embedded Julia” was generated with the algorithm: x3+3x(c -1)+(c -1)(c -2)
x0=0, xn+1=
3x2+3x(c -2)+(c -1)(c -2)
where, “c” was chosen to be near the boarder of the black region of, “Magnetic”. In both cases, “∞” and, 1 are attractors. The name, “Magnetic” comes from the fact that this algorithm is related to a physical model of magnatism, (the Potts model). For a more detailed study of those so-called, “polynomial mappings”, see for example the book, [DH]. For more examples of fractals and more detailed explainations, see for example the book, [PR]. Most algorithms used for the, “Gallery Collection” come from this book.
K
Color Management The color management of FractalDesigner handles two types of objects: color tables and color palettes. A color table is simply a set of 240 colors. There are a few predefined color tables, but you may modify them and or add your personal tables. They are universal in the sence that they belong to the application itself and are not stored within files. The color palettes are personal to each file. A color palette consists of a first color, a last color and an algorithm which interpolates from the first to the last color. For the moment being, the different algorithms are, “Linear periodic”, “Linear reverse” and “Logarithmatic”. If you plan to zoom far into the details of a given fractal, it may be convenient to choose the, “Logarithmatic” algorithm, in order to avoid too fast a change of the colors.
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Read Me’s O Designing your own Algorithms FractalDesigner comes with a, CodeWarrior Pro 5.3 project file, which allows you to compile your own algorithms. As an example the, “Douady & Hubbard” algorithm was produced by compiling the following file: #include “FractalHeader.h” void main(shortcode, FractValue*Ret, comp*z, comp*c, double*AEps, longAMax, Boolean*AInfinity, CAttracts*Attract, long*myDatas) { switch(code){ case kInit: *AInfinity=false; Attract->AddPrecompAttractor(1,false,”1”,”0”); Attract->AddPrecompAttractor(1,true,”-1/2+z”,””); Attract->AddPrecompAttractor(1,true,”-1/2-z”,””); break; case kRelease: break; case kCompute: Ret->NIter=-1; comp x=0; comp a1=-0.5+*z; comp a2=-0.5-*z; for(long i=0; i<AMax; i++){ x=x-((x-1.0)*(x+0.5+*z)*(x+0.5-*z))/(3.0*(x*x-0.25)-*z**z); if (norm(x-1.0)<*AEps){ Ret->NIter= i; Ret->NAttractor=0; return; }
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Read Me’s if (norm(x-a1)<*AEps){ Ret->NIter= i; Ret->NAttractor= 1; return; } if (norm(x-a2)>*AEps){ Ret->NIter= i; Ret->NAttractor= 2; return; } }; Ret->NIter= -1; break; } }
Let us see how this works. The, “FractalHeader.h” file contains all the useful definitions. For example, “comp” is defined to be an alias for, “complex<double>”. The arguments of the, “main” routine are... : code
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Type of action that FractalDesigner expects you to perform. It can be one of the three values shown in the listing. If, “kInit” is passed in code, you can allocate memory for personal data and put a pointer to it into, “myDatas”. This memory has to be released when the routine is called with, “kRelease” as parameter. At that time, you also have to tell FractalDesigner what are the different attractors for your algorithms by calling the, “AddPrecompAttractor” method of the, “Attract” object.
FractalDesigner 2.01 User Manual and
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z c AEps AMax
This is the variable in which you have to return the result of the computation when the routine is called with, “kCompute” in, “code”. It is a structure with three members: “NIter” contains the number of iterations, (-1 if no attractor was reached), “NAttractor” contains the number of the attained attractor, (starting at “0” for the attractors defined with, “AddPrecompAttractor” and -1 if the attractor is, “∞”), “Phase” has to contain “0” or “1” depending on how the attractor was reached. It is not obligatory to fill in this field. Contains the current value of “z”. Do not modify this value. Contains the current value of, “c”. Do not modify this value. Contains the current value of, “εε” Do not modify this value. Contains the maximal number of iterations.
Contains “1” or “0” depending whether, “∞ ” is considered as an attractor or not. You can set this value when the routine is called with, “kInit”. Attract Pointer to the list of attractors. The, “CAttracts” class is virtual and contains only one method: “AddPrecompAttractor”. See below how to use it. myDatas Pointer to a, “long” containing personal data for your routine. The, “AddPrecompAttractor” method is declared as... AInfinity
void AddPrecompAttractor(complex<double>Value, shortAnalytic, string Text1, string Text2);
Here is the meaning of these parameters: Value Value of the Attractor. If the value is an analytic expression of, “z” and, “c”, pass, “0” in this field. Analytic Pass, “true” or, “false” whether the value of the attractor is an analytical expression or not. Text1 If the value is an analytical expression, this is the string that appears in the, “Expr...” field of the, “Attractors...” dialog box. If not, it appears in the, “RE:” field. Text2 The string that appears in the, “IM:” field of the, “Attractors...” dialog box. The code resource produced this way has to be stored in a resource of the type, “FPRO” with, “ID 500”. The algorithm file has to be a file of type, “PROC” and creator, “FRAC”. It also has to contain a resource of the type, “STR#” and, “ID 128” which contains two strings. They will appear respectively in the, “ƒ(z,x)” and, “x(0)” fields of the, “Function...” dialog box. 174
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Read Me’s O Special Behaviors Here are a few things that you probably can’t guess. To zoom into the selected part, hit the return key. To get the coordinates of a specific point of a picture, hold down the, “Command” key and click onto that point. If you use the, “Full Screen” mode, you can move by using the arrow keys. To leave that mode, hit any other key, (except the return key).
S Registering The file saving, printing and, “QuickTime Export” functions are the only functions that are disabled in the demo version. Everything else can be accessed. If a function seems to be disabled, it means that it is not accessable in the current state of the program. Registering FractalDesigner enables the saving, exporting and printing functions. Moreover, you will be put into a mailing list that keeps you informed about every new version. If you want to be removed from that mailing list, just tell me at. Martin.Hairer@math.unige.ch The registration fee for FractalDesigner is, $20.00 U.S., to be paid to Kagi, not to me directly, (it costs me about $7.00 to cash a check/cheque). Kagi will provide you with a serial code, which has to be entered in the, “Registration...” dialog of the, Apple menu. If for any reason, Kagi processes your payment but does not provide you with a serial code, please send me an email and I will provide you with one. For more information about registering, see the, “Read Me (Register)” file in the, “Register” folder.
C References [DH] A. Douady and J. H. Hubbard, On the Dynamics of Polynomial-Like Mappings, Ann. scient. Ec. Norm. Sup, 4e serie, t. 18, 1985 [HW] E. Hairer and G. Wanner, Analysis by its History, Springer, 1985 [PR] H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer, 1986
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