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Daniel LordickInstitute of GeometryDresden University of Technology, Germany Rutgers University, New Jersey, May 11th 2009
Architectural Fractals
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
Pont du Gard, photograph and rendering
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5 Euro bill
Tetrahedron inside of a cube From: 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
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
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.
»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 (Sculpture in the Environment), Highrise of Homes, 1981Project, ink und charcoal 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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Architectural Fractals – Daniel Lordick, TU Dresden 22 / 42
Le Corbusier
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Architectural Fractals – Daniel Lordick, TU Dresden 24 / 42
Le Corbusier, plan voisin, Paris
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Manhattan, detail
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Manhattan, another detail
Konrad Wachsmann, wooden construction
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Skeletton of the right arm of a human
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Eiffel Tower, drawing, detail
Fractals in BerlinRiver Spree railingCieling of the New National Gallery (Mies van der Rohe)Bridge of the transportation system
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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
Architectural Fractals – Daniel Lordick, TU Dresden 35 / 42Container fractal with tubular module
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
Branching fractals, 2006
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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
