Architectural Fractals Daniel Lordick Institute of Geometry - - PowerPoint PPT Presentation

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Architectural Fractals Daniel Lordick Institute of Geometry - - PowerPoint PPT Presentation

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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

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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 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

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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, Massachusetts Institute 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

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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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»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

Highway Interstate road Main road Minor road / side street dirt road / Zufahrt Hallway / Corridor Room City planner Architect

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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

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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 Berlin River Spree railing Cieling 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

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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 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