Architectural Fractals
Daniel Lordick Institute of Geometry Dresden University of Technology, Germany
Rutgers University, New Jersey, May 11th 2009
»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
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?
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Koch curve, Koch snowflake, photographs of snow flakes
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Pont du Gard, photograph and rendering Architectural Fractals – Daniel Lordick, TU Dresden
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5 Euro bill
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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 Architectural Fractals – Daniel Lordick, TU Dresden
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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 Architectural Fractals – Daniel Lordick, TU Dresden
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Sierpinski carpet constructions on several polygons
Architectural Fractals – Daniel Lordick, TU Dresden
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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Steven Holl, Simmons Hall, Massachusetts Institute of technology (MIT) Cambridge, MA, United States, 1999-2002
Natural sponge, fractal curve
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Mikio Taka, landscape of heart, 2005 Architectural Fractals – Daniel Lordick, TU Dresden
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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.
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A sequence of scales, relevant for: Architecture World Continent Country
City planner
Region City
Architect
District / quarter Street / square / block Building / house Wing / flat Room Furniture Drawer
»Goldsmith drawings of Basle«. From: Paul Naredi-Rainer, Harmonie – Maß, Zahl und Proportion in der abendländischen Baukunst
Box
Traffic routes Highway Interstate road Main road Minor road / side street dirt road / Zufahrt Hallway / Corridor Room
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James Wines, groop SITE (Sculpture in the Environment), Highrise of Homes, 1981 Project, ink und charcoal on paper, 55,9 x 61 cm Architectural Fractals – Daniel Lordick, TU Dresden
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Louis I. Kahn, traffic scheme, project, Philadelphia, Pennsylvania, 1951-53 Architectural Fractals – Daniel Lordick, TU Dresden
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Traffic planning for Chicago Architectural Fractals – Daniel Lordick, TU Dresden
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Le Corbusier Architectural Fractals – Daniel Lordick, TU Dresden
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Le Corbusier, plan voisin, Paris Architectural Fractals – Daniel Lordick, TU Dresden
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Manhattan, detail Architectural Fractals – Daniel Lordick, TU Dresden
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Manhattan, another detail Architectural Fractals – Daniel Lordick, TU Dresden
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Konrad Wachsmann, wooden construction
Skeletton of the right arm of a human Architectural Fractals – Daniel Lordick, TU Dresden
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Eiffel Tower, drawing, detail
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Fractals in Berlin River Spree railing Cieling of the New National Gallery (Mies van der Rohe) Bridge of the transportation system Architectural Fractals – Daniel Lordick, TU Dresden
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DIN-paper format (proportion 1 : sqrt (2)
Girder fractal Architectural Fractals – Daniel Lordick, TU Dresden
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Container fractal in space (proportion: 1 / 2^(1/3) : 1 : 2^(1/3) )
Architectural Fractals – Daniel Lordick, TU Dresden
Module for the container fractal
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Container fractal with tubular module Architectural Fractals – Daniel Lordick, TU Dresden
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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 Architectural Fractals – Daniel Lordick, TU Dresden
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Y-fractal, made with a 3-d-printer at the 3D LAB B25, Institute of Geometry, TU Dresden Architectural Fractals – Daniel Lordick, TU Dresden
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Branching fractals, 2006
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Yuken Teruya, Notice-Forest 2005, cover, detail
Yuken Teruya, Notice-Forest 2004, cover, detail Architectural Fractals – Daniel Lordick, TU Dresden
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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.) Architectural Fractals – Daniel Lordick, TU Dresden
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Landscape of Corse with a fictional building
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