Final Project Parametric Design - Booklet

Fibonacci spirals, Golden spirals and golden ratio-based spirals often appear in living organisms.

Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone, and the family tree of honeybees.

WS 2016/17 22790 ASSOCIATIVE AND ALGORITMIC DESIGN

Blooming

Blooming Module Name: Associative and Algorithmic Design Module Number: 22790 Term/Year: Winter Term 2016/17 Examiner: Prof. Achim Menges Tutors: Ehsan Baharlou Institute: Institute for Computational Design (ICD)

Jakub Brahmi Nagla Gamaleldeen Adrianna Kamińska

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Blooming

Module Name: Associative and Algorithmic Design Module Number: 22790 Term/Year: Winter Term 2016/17 Examiner: Prof. Achim Menges Tutors: Ehsan Baharlou Institute: Institute for Computational Design and Construction (ICD) Jakub Brahmi Nagla Gamaleldeen Adrianna Kamińska

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Contents Chapter 01: Inspirations_________________________________________________Page 6 Chapter 02: Coding____________________________________________________Page 10 Chapter 03: Steps_____________________________________________________Page 14 Chapter 04: Shape possibilities__________________________________________Page 22 Chapter 05: Form finding_______________________________________________Page 28 Chapter 06: Shape possibilities__________________________________________Page 34 Chapter 07: Visualisations______________________________________________Page 40 Chapter 08: Model photos______________________________________________Page 44

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Inspirations Chapter XX

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CHAPTER 01

FIGURE 1: Source: https://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm Acces: 26.02.2017 XX: Description of Figure. (Source: FirstName LastName)

Inspirations The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier as Virahanka numbers in Indian mathematics.

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: 1,1,2,3,5,8,13,21,34,55,89,144

Fibonacci spirals and Golden spirals appear in nature, but not every spiral in nature is related to Fibonacci numbers or Phi. Most spirals in nature are equiangular spirals, and Fibonacci and Golden spirals are special cases of the broader class of Equiangular spirals. An Equiangular spiral itself is a special type of spiral with unique mathematical properties in which the size of the spiral increases but its shape remains the same with each successive rotation of its curve. The curve of an equiangular spiral has a constant angle between a line from origin to any point on the curve and the tangent at that point, hence its name. In nature, equiangular spirals occur simply because they result in the forces that create the spiral are in equilibrium, and are often seen in non-living examples such as spiral arms of galaxies and the spirals of hurricanes. Fibonacci spirals, Golden spirals and golden ratio-based spirals often appear in

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FIGURE 1: XX: Source: Description https://www.emaze.com/@AFOZWLRZ/Presentation-Name of Figure. (Source: FirstName LastName) Acces: 26.02.2017

living organisms. Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone, and the family tree of honeybees. However, numerous poorly substantiated claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g., relating to the breeding of rabbits in Fibonacci’s own unrealistic example, the seeds on a sunflower, the spirals of shells, and the curve of waves In our first task we aimed at designing an abstract figure that is visually attractive. We looked through nature as it is a great source of revealing geomtric inspirations. Seeing the aesthtics of the mathematical proportions of The Golden ratio, fibonacci sequence was our tool to reach it.

References John Hudson Tiner (200). Exploring the World of Mathematics: From Ancient Record Keeping to the Latest Advances in Computers. New Leaf Publishing Group.

ISBN 978-1-61458-155-0.

AAD Algorithms-Aided Design. Parametric strategies using Grasshopper, 1st edition, Edizioni Le Penseur (2014), England, ISBN 978-8895315300 http://modelab.is/grasshopper-primer/ Acces : 26.02.217

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Coding Chapter XX

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CHAPTER 02

Fibonacci sequence

Controlling the spiral

Separate mesh faces

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Steps I STEP

III STEP

Creating Fibonacci sequence in 2D. Making series of a numbers with a sepcific values. Connecting series of a number with mathematical expression. The result of the expression are points in (x,y) direction as a spiral.

Remove the unwanted connections by culling pattern.

Connecting constructed points with cull bottom. Shifting multiple times order of the points to get all possible spirals of a kind.

II STEP Creating Fibonacci in 3D. Making sereis of a number with specific values. Connecting series of a number with a graph mapper which enable changing shape in z-direction.

V STEP Define (0,0,0) point as a beginning. Create a mesh from the lines. Explode lines the the curve into smaller segments. Remove similar lines from the list. Transform list of lines in a mesh. Decompose a mesh into ist faces and after into its component parts.

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Curve using predefined points

Sun vector

Sorting vertices of mesh faces

Smoothness and wall thickness

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VI STEP

IX STEP

Creating attractor curve(a circle), then finding points on it closest to face vertices.

Sorted vertices of a mesh faces. Retreive all the corner from the separate meshes.

VII STEP

X STEP

Connection of face vertices and their closest points with lines. Then measuring the lenghts of lines and using sort list to organize indexes of face vertices according to their distance from attractor curve.

Sun dependence. Making a moveable point on a cirlce as a sun. Making a vector between point and moveable item from IX STEP. Change the lenght of a curve.

VIII STEP Sorting vertices of mesh faces.

XI STEP Creation of a new moveable surface which are depndet on the sun. Adding smoothing and wall thickness.

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Steps Chapter XX

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CHAPTER XX 03 CHAPTER

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CHAPTER XX 03 CHAPTER

03 CHAPTER XX

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CHAPTERXX 03 CHAPTER

CHAPTERXX 03 CHAPTER

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Shape possibilities Chapter XX

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CHAPTER 04 XX

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Form finding Chapter XX

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CHAPTER 0 05

Fibonacci sequence

Sphare closes points

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Controlling the spiral

Separate mesh faces

CHAPTER05 XX CHAPTER

Curve using predefined points

FIGURE XX: Description of Figure. (Source: FirstName LastName)

Sorting vertices of mesh faces

Smoothness and wall thickness

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CHAPTER 05 XX

CHAPTER CHAPTER05 XX

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Shape possibilities Chapter XX

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Visualisations Chapter XX

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Model photos Chapter XX

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CHAPTER 08 XX

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CHAPTER 08

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CHAPTER 08

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Fibonacci spirals, Golden spirals and golden ratio-based spirals often appear in living organisms.

Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone, and the family tree of honeybees.

WS 2016/17 22790 ASSOCIATIVE AND ALGORITMIC DESIGN

Blooming

Blooming Module Name: Associative and Algorithmic Design Module Number: 22790 Term/Year: Winter Term 2016/17 Examiner: Prof. Achim Menges Tutors: Ehsan Baharlou Institute: Institute for Computational Design (ICD)

Jakub Brahmi Nagla Gamaleldeen Adrianna Kamińska