NAVIGATING
the INFINITE SURFACE
Rory Noble-Turner
Magnetism
m Studies
0.0s
1.0s
2.0s
5.0s
6.0s
7.0s
10.0s
11.0s
12.0s
15.0s
16.0s
17.0s
Polar Interacti
Under the influence of two magnetic distorting and morphing as the p
ion Over Time
c fields the magnetite dust coalesces, poles interact with one another.
3.0s
4.0s
8.0s
9.0s
13.0s
14.0s
18.0s
19.0s
2.0s
3.0s
Revealing the
Plotting the field lines re logic governing the m
e Field Lines
eveals an organisational magnetic interations.
4.0s
Flatter, more layered
Spread out, Jagged stalacmite formations
A
B
Evolution of magnetite formation
C
A
B
Decreasing magnetic fie
Microscopic Fra
Under the influence of a strong magnetic field the m emanate from the poles, transitioning in structure
d flake-like structures
C
eld influence
actal Formation
magnetite dust forms distinct fractal structures that e as the strength of the magnetic field dissipates.
Fine, condensed filaments form distinct surface boundary
B
A
C
Tiling Systems W
A variable scale tiling system is arrayed replicate the clustering and fragmented
A
B
C
D D
Within the Field
d along the field lines in an attempt to d nature of the magnetised iron filings.
Varying Tile D
Porosity of the arrayed geometry change
Density & Scale
es as the tile density and scale is altered.
Spatial Opportunitie
Spaces are categorised by blurre and interior, demonstrating a ba
es within the System
ed boundaries between exterior alance between chaos and order.
Inhabiting
Spaces and forms e forces acting beyo
the Vortex
emerge from hidden ond our awareness.
Field Networks
s & Trajectories
Field Lines as Spa
Viewing the field vector lines quality, displaying areas of den
atial Organisation
in plan gives them a spatial nsity and porosity within space.
d
3r d
2n
Ge
ner
atio
n
No t
1s
Magnetic Field
The relationship between attractor and repellor pole The field lines were further manipulated through
e on
d Simulations
es was analysed through magnetic field simulations. the application of an electromagnetic spin force.
al c i t Ver
45
r c
e
tal n zo
F
o
S
n
ri
D
pi
Ho
es e r eg
Magnetic Field
As individual objects the field models appea
d Study Models
ar as possible architectural ornamentation.
Porosity o
As the field lines coalesce and unravel fr planar surface and linear form emerge
of Surface
rom one another, a relationship between es, creating dynamic spatial divisions.
Magnetic Fie
Combining the field lines into a larger controlled of space. Further layering of frozen field lines al
eld Networks
d network creates a more coherent organisation llows for a more precise creation of form.
A - Gradual gradient in density between internal and external space
B - Thicker, more relatively cons
Curating Fl
Experiments in construc flow intensity and s
e entangled flow, sistent density
low Density
cting regions of varying spatial organisation.
C - Circulation around central vortex, stark contrast between areas of low/high density
Blurred Spatia
Sectioning the field network allows us arise, characterised by blurred spatial bo
al Boundaries
to understand the internal spaces that oundaries between interior and exterior.
Fractal Geometry & T
The Infinite Surface
Example L-System, M
The distinguishing characteristic of L-Systems is that all rules are applied in parallel for each generation. Despite their simplicity this makes L-Systems very powerful. Their languages may contain intricate patterns with infinitely varying subtlety.
Seed: A Rules: A= B = string
A AB ABBA ABBABAAB ABBABAABBAAB Heighway Dragon Curve S: FX R1: X=X+YF+ R2: Y=-FX-Y Generations 2,4,8,12 90° Segment Angle
60° Segment Angle
Koch Curve FD: 1.26
Minkows FD:
Fractal Generation &
Space-filling curves are a simple example of line dimension to infinity, through the repetition of
Morse-Thue System:
= AB = BA
generation
BABBA
0 1 2 3 4
120° Segment Angle
ski Curve : 1.5
Peano Curve FD: 2.0
Space Filling Curves
ear fractal geometry which grow beyond the 1st simple rules dictated by Lindenmayer Systems.
S: FX R1: X=X+YFR2: Y=-FX-Y 12 Gen. 4,096 line segements
50°
60°
S: FX R1: X=X+YF+ R2: Y=-FX-Y+F 12 Gen. 6,143 line segments
60°
30°
S: FX R1: X=X+YF+Y R2: Y=-FX-Y-F+X+Y 12 Gen. 13,633 line segments
30°
80°
Fractal Curv
Alterations to the formula of 2 results in radical variations in
ve
70°
90°
89°
Evolution
2 dimensional L-system curves n the fractal curve geometry.
90°
80°
120°
90°
170°
3D mandelbulb for the Mandelbrot Set, F(x)=x2+c
The below image is the first ever visualisation of the most famous 2D fractal, the Mandelbrot Set, first viewed in 1980 by reknowned Mathematician Benoit Mandelbrot. The geometry exhibits infinite density, volume and surface area allowing one to zoom into the fractal forever, discovering new forms.
Mandelbulbs & 3D
Harnessing the Mandelbulb generate and manipulate
Fractal Generation
3D programme in order to e 3D/4D fractal geometry.
Harsh ripples and tears violently collide and dissolve.
Hopf 4D
Surfaces flow and coale
Magnetic
Mandelbulb For
Each formula generates distinct f mimic geometries and phenome
esce along vector lines
c Field 3D
rmal Properties
formal and spatial properties that ena present throughout nature.
Thin layers and skins overlap and fold over one another
Mandelbrot Set 3D
Three base mandelbulb fractals were initially mixed, subsequent species of mandelbulbs were pursued based on a spatial investigation of their internal structure, and whether the forms resembled the flowing, twisting nature of the magnetic field studies.
Mixing Mandel
New more desirable geometry can be genera in different ratios, altering various parameter several generations a more co
lbulb Formulas
ated by mixing multiple mandelbulb formulas rs such as Julia Value and Fractal Ratio. After ontrolled outcome is achieved.
The generative design research projects of Michael Hansmeyer try to understand how to create immense formal complexity through simple iterative processes.
Geometric Fold
Flowing forms weave their way creating layered spatial division
ds and Layering
y through the fractal structure, ns that gently part and separate.
The swiss pavilion for the 2016 Venice Architecture Bienalle, by architect Christian Kerez creates a cavernous space formed from panels of sprayed fibreglass cement, finished with plotting and milling techniques.
Printing the Fr
SLS printing the fractal mesh reveals the highly te
Fractal Artefact
extured surfaces and tight folds of the geometry.
Fractal
l Flows
Section A
Sectioning the
When sectionioned, the mandelbul that are formed by the twisting
Section B
A
B
e Mandelbulb
lb reveals complex internal spaces g and folding of the geometry.
Twisting Surfaces an
Tendrils and thin filaments stret dense and porous geom
nd Formal Layering
tch and overlap as the infinitely metry folds in on itself.
Understanding the Spati
Sectioning the mesh in multiple the complex spaces that arise
ial Qualities of the Mesh
e directions reveals more clearly e within the generated fractal.
Slicing the F
Slicing the fractal at regular interv of the geometry and how it is
Fractal Mesh
vals reveals the contorting nature s twisting through the fractal.
Surface Fold Ge
eometry Studies
Twisted Surfaces &
Exploring layering of surfac
& Folded Geometry
ces and intertwining skins.
Layered
Intersticial spaces arise betweeen th that is continuously split and defin
d Skins
he layers, creating a continous space ned by twisting, entangled surfaces.
Interstitial Space
By building out from one of the fractal slices, th how spaces could be more clearly defined th
es within the Fold
his 1:20 sectional study attempted to understand hrough the layering and overlapping of skins.
Inhabiting
As the surfaces overlap and flow a spaces develop, from narro
the Layers
along one another, heterogeneous os gaps to cavernous voids.
Spatial Sect
Combining the field network fl techniques in order to create mo
tional Study
flow studies with surface fold ore distinct architectural spaces.
Final Model - Subway Tr
The model adopts the programme of a explore how an architecture can commu flow through layering of surface
ransportation Hub Study
subway transportation hub in order to unicate movement and direct circulation es and formalised field networks.
Rory Nob
ble-Turner
P
Site Ov
layers of history and cul
P
verview
lture delicately coalesce
P
Locating Pino Su
Located in the city’s historic centre, the site s a hub of activity home to a large local ma
P
uarez, Mexico City
sits in the popular tourist area of Pino Suarez, arket, public plaza and vital metro station.
P
2
Cuatro Caminos
1
Observatorio
Tasq
Pino Suarez, A ke
Located at the intersection of the city’s two of cultures, catering to the influx of tourists to the north, and poorer lo
P
Pino Suarez Pantitlan
quena
ey Urban Junction
o busiest lines, the site is a key convergence s and commuters from the historical centre ocal residents to the South.
P Agrarian Museum
Chapel of St Luke
Pino Suares Market
E
A Convergence of H
The site’s urban and historical context m cultures and histories mix among
P Pino Suarez Bus Terminus
Ehecatl Shrine
Religious Office & Retail Indoor Market Residential Green Space
History and Culture
makes it a key junction where contrasting gst the relentless flow of people.
Offices of the Parish of St Michael
P
A - Toward the Market
B - North Entrance
C - South Entrance
B
Plaza in Need o
The Southern entrance to the site is un Underpass, making it far less inviting tha
P
A
C
of Rejuvenation
nkept, and bordered by a busy Highway an the frenetic, open northern entrance.
P Walkways to South and West, funnel commuters across the busy highways
e
oT
y Fra
d van Ser
eir
eM
ad res
ĂŠ
Jos
ga
aza
a Iz
rĂ Ma
an
ri
st
de
Pe ow
Fl
2
3
rd
busiest station in the system
60,000,000 Commuters, pass through the station annually
Pino Suarez Me
The complex nature of the site means the st flow. Commuters, marketeers and tou
P
etro Circulation
tation has to cater for very heavy pedestrian urists mix in a very concentrated area.
Zocalo Historical Centre
13 minutes 0.6 miles
Main entrances to the north cater for the high rate of flow from the busy historic centre
Jos éM
arí aP ino
Pino Suarez Plaza
Suá rez
1
An underground tunnel containing cafes and shops connects the station to the next stop on line 1, Zocalo.
P
Existing Az
The Aztec altar was in honor of the Wind God Rain God. Sacred offerings to the Gods would
P
Late 1400s Ehecatl, Wind God
Mid 1400s
Early 1400s Tlaloc, Rain God
ztec Shrine
d Ehecatl, who signalled the arrival of Tlaloc the d be placed on top of the altar during worship.
The altar was constructed out of volcanic rock in stages over a 100 year period. Thus the shrine’s form and orientation evolved in accordance with its religious meaning at that period.
P
5oth Anniversary of th
During construction of the original station in The artefact was relocated in order to allow
P
he Artefact’s Discovery
n 1968, an ancient Aztec altar was unearthed. the metro station construction to continue.
P
A Geometry Repr
With its distinct circular geometry, the des immortality, and the infinite nature of ti
P
resenting Infinite
sign of the shrine was intended to represent ime and the universe created by the gods.
Severe Overheating
Run-down Market
The cramped concourses restrcit flow and become very hot during the day
The current market is confined to a run-down temporary structure which blocks access to site
Overcapacity Station
Neglected H
Site Weaknesses
The site offers many pos new, more exciting public
Forgotten Shrine
Inadequate Entrances
The Aztec shrine is hidden away from view with no dedicated viewing space
The few narrow entrances are insufficient to deal with the increasing number of commuters
Historic Site
& Opportunities
ssibilities for designing a c plaza and metro station.
Restricted Access & Noise/Air Pollution
Proposal - The Unf
constru o demol
finished Excavation
ucted? or lished?
New Metro Line The insertion of a new metro platform 20m beneath ground level will aim to alleviate the currently overburdened network by expanding the Pino Suarez station.
Subterranean
A public market space is i level as a retreat from th ways above and searing h
Three Programm
The scheme proposes the deve which will each inhabit a pre These cuts will form the basis
n Public Plaza
inserted beneath ground he bordering noisy highheat of the Mexican sun.
mes, Three Cuts
elopment of three programmes ecise cut made into the site. s for a subterranean proposal.
Altar Exhibition/Celebration Space The altar will be returned to its original site of discovery 50 years prior and placed upon a bespoke pedestal watching over the site. Thus reestablishing its importance in the site.
Pino Suarez: Now
+15 y
Lan
Me
Ma
The 4-Dimensio
The excavation of the site will occu of time whilst remaining hab
years
ndscaped Plaza
etro Space
arket Place
onal Excavation
ur in stages over a sustained period bitable for the general public.
+25 years
The Temporary
a dense network hung overhead concea
y Construction
aling a landscape as it morphed beneath
P
Site cleared and geologically mapped
Exploratory vertical shafts excavated
Open excavation
Stages of Erecting the T
A lightweight architecture is constructed du stages to ensure minimal disruption
P
n begins
Temporary Construction
uring the landscaping and deep excavation n to the public’s access to the metro.
Overhead public walkways installed
Addition of shaders and lightweight shelters
P Large canopies conceal the rejuventation process from highway passers-by as well as direct cooling wind down into the construction site
Lightweight shaders protect visitors from the harsh Mexican sun
Excavation aro the Aztec shri
Concealing the
The temporary construction conceals the excavat phase, keeping them cool as well as hiding certain a
P
ound ine
Walkways circulate around the altar excavation and allow views down into the construction site whilst funnelling commuters down into the still operational metro lines
e Rejuvenation
ted areas beneath during the open construction areas from the public creating a sense of suspense.
Vehicle route down into the centre of the site allows the easy transport of construction materials and machinery
Machinery access
P
A Vehicle routes carve through the site, transporting material and machinery
B
Walkways meander across gaping chasms.
B
C
Coinhabiting the C
Public walkways meander through the occurs beneath. The construc
P
C
.
Large canopies and shaders conceal certain construction stages.
A
Construction Site
e site, as excavation and landscaping ction site is a hub of activity.
P
A Rare Glimspe of a
As earth around the altar i is prepared for a return
P
a Future Monument
is removed, the monument n to its site of discovery.
Massing & C
These experiments looked at mented lining shafts as a me
Cut Iterations
using vertical, circular segeeans of cutting into the site.
Early Conce
eptual Plan
10m
Generating the F
An artefact from the digital
Future Artefact
l turn, an algorithmic fossil
Ancient Aztec Shrine The ancient artefact, a representation of infinite
A Reinterpreta
Whereas the Aztecs created an architecture re generated fractal geometry gives rise to
Generated 4-Dimensional Fractal The future artefact, the algorithmic manifestation of infinity
ation of Infinite
epresenting infinite using euclidean geometry; o an architecture resulting from infinity.
3D mandelbulb for the Mandelbrot Set, F(x)=x2+c
The below image is the first ever visualisation of the most famous 2D fractal, the Mandelbrot Set, first viewed in 1980 by reknowned Mathematician Benoit Mandelbrot. The geometry exhibits infinite density, volume and surface area allowing one to zoom into the fractal forever, discovering new forms.
3D Fractals and the
Harnessing the Mandelbulb generate and manipulate
e Infinite Geometry
3D programme in order to e 3D/4D fractal geometry.
Three base mandelbulb fractals were initially mixed, subsequent species of mandelbulbs were pursued based on a spatial investigation of their internal structure, and whether the forms resembled the flowing, twisting nature of the magnetic field studies.
Attempts at Recreatin
Fractals were generated with the aim of recreati formations found in rock and large geologi
ng Geological Layering
ing the types of twisting strata and sedimentary ical landforms such as the vermillion cliffs.
Understanding the Spati
Sectioning the mesh in multiple the complex spaces that arise w
ial Qualities of the Mesh
e directions reveals more clearly within the generated landscape.
Fractal Textu
When 3D printed we can see the tight
ural Qualities
t folding of surfaces and rich textures.
Tit
Explan
tle
nation
Placing Fragm
ments on Site
10m
Planting the Fu
the site submitted as an archit
uture Artefact
tecture was delicately inserted
New architectural insertion
Ticket barrier Existing station concourse
Existing Station concourse
The Excavation/Con
Interesting relationships occur b languages and strategies as the and the excavated
Excavation Area
Glass walkway over excavation
Excavated evolving landscape
nstruction Boundary
between conflicting architectural e existing station is dismantled, d landscape grows.
A
B
Glass walkways guide metro commuters across the excavated earth
Channelled water negotiates between the realm of construction
A
B
Signalling a Transition t
Close ups of the fragment model r the construction and excavation i the ticket barrier as well as ch
C
n and excavation
C
through Material Details
reveal how the transition between is signalled by the positioning of hanges in material and texture.
Ticket barrieris placed along the boundary, signalling the transition from one realm to the next
Traversing the Exc
Glass walkways delicately negotiate t upon steel piles, which firmly
cavated Landscape
the excavated earth below supported y secure the ground beneath.
Excavating the Fut
a carefully choreographed erosio
ture Architecture
on, a gradual sculpting of space
A
B
D
E
A - Generated vortex fractal to be embedded B - Prints placed within mould C - Pouring of the plaster mix D - Set cast E - Cast cut in half F - Chiselling out the softer plaster
Embedding and Exca
A 3D printed fractal fragment was embedde was then sectioned in half before the fractal w
avation Experiments
ed in consecutive layers of plaster. The cast was delicately chiselled out to create spaces.
C
F
Material and Te
The layers of plaster form stria of the implanted geometry, cre natural patterns
extural Layering
ations that follow the outlines eating delicate whorls and fine at the boundary.
Light areas harder, more resistant to excavation Red areas softer, more likely to crumble
Placing Points of
f Site Excavation
10m
Subterranean
A hidden world chisslled from th
n Exploration
he earth, a realm of discontinuity
Probing t
The plaster block was quarter into to reveal the insertions wi
the Fossil
red and each element carved ithin and new possible spaces.
Generating Space th
Various experiments looking at sub whilst simmultaneously installing
hrough Subtraction
btracting material to create space g services and bespoke insertions.
+2 yrs: Inital Vertical Excavation & Soil Analysis
+ 20 years: Horizontal Excav
Long Term Sculp
Over time the subterranean spac geological and infrastructu
vation & Platform insertion
pting of the Earth
ces evolove as the programmatic, ural requirements change.
+ 50 years: Programmatic Expansion requires further excavation
Massing & C
Experimenting with linear cuts aligned t running parallell to the existing and
Cut Iterations
to a diagrid system with the x and y axis d proposed metro line respectively.
Exploring Subt
terranean Plans
10m
Step down: 0.8mm Step over: 1mm Max depth: 4.5mm Cutting Time: 3.5 hrs
1:1 CNC Ston
An experiment into CNC stone milling was c within the rock could act as a key driver f
ne Excavation
carried out to understand how the striations for the drilling and excavation strategies.
A Clash of Text
The nature of milling results in an interes
ture and Form
into the rough stone sting discontinuity.
Massing & C
The excavation was reduced to two linear c into how a landscaped ground pl
Cut Iterations
cuts and one square cut, with explorations lane could lure visitors beneath.
Early A2 S
Section
A Commute Throug
a carefully choregraphed erosio
gh The Excavation
on, a gradual sculpting of space
Services and storm drainage pipes are exposed udring excavation
Previously inserted piles are later excavated around as spaces grow
Subterrane
Subsurface services and structural systems are expos
ean Spaces
sed during the excavation beginning to define spaces.
Exposed grouting system
The remnants of abandoned tunnelling attempts
Inside the Exca
Views across the central cu floor give a sense of in
avated Crevasse
ut and up from excavation nhabiting the crevasse.
Smooth, East-West cut fo
Resolu
a carefully choregraphed erosio
or efficient metro
lution
on, a precise scarring of the land
Jagged, North-South scar for chaotic market
Planning
Probing and test trenches
Choreographing
Over time the excavation site evolves a layers of information condense a
g the Excavation
above and below as the plaza expands, as more information is obtained.
Deep Vertical Shafts
Horizontal subsurface excavation
1.
The Altar in Comman
Multiple iterations of cuts were made into the si
10.
nd of the Excavation
ite whilst the altar watched over the excavation.
The three cuts are made into the site
The earth is secured by extensiv
A
B
C
Stages of Achievin
Over time key stages occur, layeri
ve piling and bracing
A central winding walkway is inserted, connecting the excavated spaces and leading to the altar.
An open pool of water is placed on the ground level, helping to cool the excavated spaces beneath, and resurrect the water God, to which the altar is dedicated.
Combined Proposal
D
ng the Architecture
ing up to form the final proposal.
E
Nested in the City li
Nested within a tranquil pool the arch within the city, a future artefact givi
ike a Precious Jewel
hitecture and altar embed themselves ing glimpes of a subterranean realm.