Polygonal Growth by Matthias Behrmann

Polygonal Growth

Trans-Scalar Diversity / Microclimatic Articulations Matthias Behrmann Architecture and Performative Design 2014-15

The notion of Low Poly

NEXT Generation Cover, 1997

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

References

F117 Stealth Fighter

Oporto Vodafone Building, Barbosa & Guimaraes of Matosinhos

Nike Chuck Posite QS iD

Lexus SUV Concept study

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

United Nude ‘Lo Res Car’

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Timothy J. Reynolds ‘Polygon Bear’

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

First manual Setup of a Tessellated System

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

‘The Lonesome Tree’, Caspar David Friedrich

original painting

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

work in process

made by hand

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

scripted

Trans-Scalar Diversity in Trees

1000000000

100000000

10000000

1000000

100000

10000

1000

100

Ginkgo at Nizza river banks, Frankfurt

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

veines

leaves

buds

branchlet n°2

branchlet n°1

branches

trunk

clustered leaves

straight-lined trunk

clustered leaves growing out of the buds

branchlet as extension out of old bud

stacked buds

branchlet

branching density

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

transitions in scale/branching

Ginkgo leaf / autumn colour

20 Ginkgo leaves

color palette autumn leaves

Ginkgo biloba fruit

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

traced leaves overlay

Sequence of Morphogenesis

voronoi generation 1 point distribution: homogeneous

voronoi generation 1 point distribution: contracted

voronoi generation 1 point distribution: homogeneous

voronoi generation 2 unit count: 2 point distribution: --point count: ---

voronoi generation 2 unit count: 2 point distribution: homogeneous point count: 20

voronoi generation 2 unit count: 8 point distribution: homogeneous point count: 20

face normals length: ---

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

voronoi generation 1 point distribution: homogeneous

voronoi generation 2 unit count: 29 point distribution: homogeneous point count: 20

face normals length: ---

face normals length: 0.5

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Void study of the Commerzbank Tower, Frankfurt

section

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

full building

vertical section cut

full building

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

vertical section cut + VOID

vertical section cut

VOID

Highrise Design

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Main vertices

Insertion Points

About Brownian Motion

Same module under the effect of different insertion points

Diffusion of lines from the experiment a

Insertion Point

a’

a’’

Insertion Point

c b’ c’’ d

b’’

Insertion Points

e’’ f’’

Axial Tran

c’

Variations x’

d’ e

e’

d’’

f’

g’’

y’

z’

Axial Translation

Domain Overlap Depends on Intensity of the insertion point

h’’

o’

x’

Variables

g’ i’’

g x

h’

x’

Distance xy and x’y’ determine the outcome which is related t i the insertion point intensity and vary with density of the material

x’ y’

i’

y’

h y

z’

Potential Generation Points

z o

o’

x’

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APDx2014-15 x’

Variables

Primary Generation Points

Serves as the basis for arc genration

Evolution Steps

accretion count: 10

accretion count: 50

accretion count: 100

accretion count: 500

accretion count: 1000

accretion count: 1500

accretion count: 2000

accretion count: 2500

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

accretion count: 3000

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

accretion count: 3500

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

United Nude ‘Lo Res Car’

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Low Poly Through Mesh Reduction

vertices: 92 faces: 180 reduction: 0

vertices: 72 faces: 140 reduction: 20

vertices: 52 faces: 100 reduction: 40

vertices: 32 faces: 60 reduction: 60

vertices: 12 faces: 20 reduction: 80

vertices: 216 faces: 300 reduction: 0

vertices: 213 faces: 254 reduction: 40

vertices: 209 faces: 212 reduction: 80

vertices: 196 faces: 166 reduction: 120

vertices: 165 faces: 100 reduction: 160

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Surface Exploration First Year Project

one fold, one pleat, same direction + one fold in cross direction

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

landscape test, summer semester 2014

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

The Garden Archive

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Gartenstraße

Site Plan

Dürerstraße

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Low Poly Body Growth Studies

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 2000

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 1500

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 1000

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 750

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 500

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 300

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 200

proximity: 2,000 pull: 0,250 wander: 0.000 spin: 1.000 steps: 100

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 2000

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 1500

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 1000

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 750

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 500

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 300

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 200

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 1.000 steps: 100

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 2000

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 1500

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 1000

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 750

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 500

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 300

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 200

proximity: 2,000 pull: 0,500 wander: 1.000 spin: 2.000 steps: 100

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Seed Bodies For the Building Volumes

point distribution

growth paths

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

volume generation

Temperature Sensing

0 0

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

120

depth frames Outer Layer tilted surfaces

stellated surfaces

Full Building

display Inner Layer conference greenhouse archive

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Trans-Scalar Diversity – Element Catalog and System Composition

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Scalar Comparison of System

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Top View

sac

TRANS-SCALAR DIVERSITY / POLYGONAL GROWTH / MATTHIAS BEHRMANN / APD 2014-15

Overall Section

conference