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Daniel Lordick

Institute of Geometry

Dresden University of Technology, Germany

 Rutgers University, New Jersey, May 11th 2009

Architectural Fractals

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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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Koch curve, Koch snowflake, photographs of snow flakes

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Pont du Gard, photograph and rendering

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5 Euro bill

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Tetrahedron inside of a cubeFrom: Zeitler/Neidhardt: Fraktale und Chaos

Stars by M.C. Escher

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

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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

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

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Fractal of the Oktahedron, steps 1, 2 and 3

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

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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

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Mikio Taka, landscape of heart, 2005

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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

Lab Architecture Studio

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Lab Architecture Studio,Ronald Bates und PeterDavidson: MelbourneFederation Square, 1997-2002

The façade makes use of thePinwheel tiling, an aperiodictiling proposed by JohnConway and Charles Radin.

A sequence of scales

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»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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James Wines,groop SITE (Sculpturein the Environment),Highrise of Homes,1981Project, ink undcharcoal on paper,55,9 x 61 cm

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

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Traffic planning for Chicago

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Le Corbusier

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Le Corbusier, plan voisin, Paris

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Manhattan, detail

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Manhattan, another detail

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Konrad Wachsmann, wooden construction

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Skeletton of the right arm of a human

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Eiffel Tower, drawing,detail

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

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Girder fractal

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

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

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Container fractal with tubular module

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Cantor set (preserves area)Cantor dust in two dimensions

Castle fractal, based on the two-dimensional Cantor dust

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Pythagorean trees and tiling

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

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Branching fractals, 2006

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Yuken Teruya, Notice-Forest 2005, 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