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Daniel Lordick Institute of Geometry Dresden University of Technology, Germany Rutgers University, New Jersey, May 11th 2009 Architectural Fractals

Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Page 1: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Daniel LordickInstitute of GeometryDresden University of Technology, Germany Rutgers University, New Jersey, May 11th 2009

Architectural Fractals

Page 2: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Principles of Construction

Iteration

Self-similarity

Scaling

Questioning

Which phenomena in nature, technology and design show these principles?

How strict can the principles be applied?

How can the principles be systematized?

»As far as mathematical theorems are dealing with reality, they are not certain, and in so far as they are certain, they

are not related to reality.«Albert Einstein, 1921

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Page 3: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Koch curve, Koch snowflake, photographs of snow flakes

Page 4: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Pont du Gard, photograph and rendering

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Page 5: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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5 Euro bill

Page 6: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Tetrahedron inside of a cube From: Zeitler/Neidhardt: Fraktale und Chaos

Stars by M.C. Escher

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Page 7: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Fractal of the tetrahedron, steps 0 to 3, the first step is the Stella Octangula

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Page 8: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Fractal of the cube, three-dimensional analogon to the Koch curve, Illustration from: Zeitler/Neidhardt, Fraktale und Chaos – eine Einführung

Rendering after four iterations

Kazimir Malevich, Architecton

Page 9: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Koch curve of regular hexagons in steps 1 through 3. From: Zeitler/Neidhardt, Fraktale und Chaos

Page 10: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Fractal of the Oktahedron, steps 1, 2 and 3

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Page 11: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Sierpinski carpet constructions on several polygons Menger sponge, the fourth iteration of the construction process

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Page 12: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Proposal for a fractal roof according to the sierpinski carpet

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Natural sponge, fractal curve

Steven Holl, Simmons Hall, MassachusettsInstitute of technology (MIT)Cambridge, MA, United States, 1999-2002

Page 14: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Mikio Taka, landscape of heart, 2005Architectural Fractals – Daniel Lordick, TU Dresden 14 / 42

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Pinwheel fractal. Being obtained from substitutions, the pinwheel tiling can also be seen as a fractal.

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Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation Square, 1997-2002

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Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation Square, 1997-2002

The façade makes use of the Pinwheel tiling, an aperiodic tiling proposed by John Conway and Charles Radin.

Page 18: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

»Goldsmith drawings of Basle«. From: Paul Naredi-Rainer, Harmonie – Maß, Zahl und Proportion in der abendländischen Baukunst

A sequence of scales, relevant for:Architecture

World

Continent

Country

Region

City

District / quarter

Street / square / block

Building / house

Wing / flat

Room

Furniture

Drawer

Box

Traffic routes

HighwayInterstate roadMain roadMinor road / side streetdirt road / ZufahrtHallway / CorridorRoom

City planner

Architect

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Page 19: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

James Wines, groop SITE (Sculpture in the Environment), Highrise of Homes, 1981Project, ink und charcoal on paper, 55,9 x 61 cm

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Page 20: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Louis I. Kahn, traffic scheme, project, Philadelphia, Pennsylvania, 1951-53

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Page 21: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Traffic planning for Chicago

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Page 23: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Le Corbusier

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Le Corbusier, plan voisin, Paris

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Manhattan, detail

Page 29: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Manhattan, another detail

Page 30: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Konrad Wachsmann, wooden construction

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Skeletton of the right arm of a human

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Eiffel Tower, drawing, detail

Page 32: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Fractals in BerlinRiver Spree railingCieling of the New National Gallery (Mies van der Rohe)Bridge of the transportation system

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Page 33: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Girder fractal

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DIN-paper format (proportion 1 : sqrt (2)

Page 34: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Container fractal in space (proportion: 1 / 2^(1/3) : 1 : 2^(1/3) ) Module for the container fractal

Page 35: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Architectural Fractals – Daniel Lordick, TU Dresden 35 / 42Container fractal with tubular module

Page 36: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Cantor set (preserves area)Cantor dust in two dimensions

Castle fractal, based on the two-dimensional Cantor dust

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Page 37: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Pythagorean trees and tiling

Page 38: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

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Y-fractal, made with a 3-d-printer at the 3D LAB B25, Institute of Geometry, TU Dresden

Page 39: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Branching fractals, 2006

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Page 40: Architectural Fractals · 2015. 7. 9. · Architectural Fractals – Daniel Lordick, TU Dresden 17 / 42 Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation

Yuken Teruya, Notice-Forest 2005, cover, detail

Yuken Teruya, Notice-Forest 2004, cover, detail

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Town hall Osnabrück, Lower Saxonia, window

(One Location of the end of the Thirty Years‘ War.On 15 May 1648, the Treaty of Osnabrück was signed.)

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Landscape of Corse with a fictional building