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? 2 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Koch curve, Koch snowflake, photographs of snow flakes 3 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Pont du Gard, photograph and rendering 4 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
5 Euro bill 5 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Tetrahedron inside of a cube From: Zeitler/Neidhardt: Fraktale und Chaos Stars by M.C. Escher 6 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Fractal of the tetrahedron, steps 0 to 3, the first step is the Stella Octangula 7 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
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 8 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Koch curve of regular hexagons in steps 1 through 3. From: Zeitler/Neidhardt, Fraktale und Chaos 9 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Fractal of the Oktahedron, steps 1, 2 and 3 10 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Sierpinski carpet constructions on several polygons Menger sponge, the fourth iteration of the construction process 11 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Proposal for a fractal roof according to the sierpinski carpet 12 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Steven Holl, Simmons Hall, Massachusetts Institute of technology (MIT) Cambridge, MA, United States, 1999-2002 Natural sponge, fractal curve 13 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Mikio Taka, landscape of heart, 2005 14 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Pinwheel fractal. Being obtained from substitutions, the pinwheel tiling can also be seen as a fractal. 15 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Lab Architecture Studio, Ronald Bates und Peter Davidson: Melbourne Federation Square, 1997-2002 16 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
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. 17 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
A sequence of scales, relevant for: Architecture World Continent City planner Country Region City Architect District / quarter Street / square / block Building / house Wing / flat Room Furniture »Goldsmith drawings of Basle«. From: Paul Naredi-Rainer, Harmonie – Maß, Zahl und Proportion in der abendländischen Baukunst Drawer Box Traffic routes Highway Interstate road Main road Minor road / side street dirt road / Zufahrt Hallway / Corridor Room 18 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
James Wines, groop SITE (Sculpture in the Environment), Highrise of Homes, 1981 Project, ink und charcoal on paper, 55,9 x 61 cm 19 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Louis I. Kahn, traffic scheme, project, Philadelphia, Pennsylvania, 1951-53 20 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Traffic planning for Chicago 21 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
22 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Le Corbusier 23 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Le Corbusier, plan voisin, Paris 24 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
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27 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Manhattan, detail 28 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Manhattan, another detail 29 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Konrad Wachsmann, wooden construction Skeletton of the right arm of a human 30 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Eiffel Tower, drawing, detail 31 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Fractals in Berlin River Spree railing Cieling of the New National Gallery (Mies van der Rohe) Bridge of the transportation system 32 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
DIN-paper format (proportion 1 : sqrt (2) Girder fractal 33 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Container fractal in space (proportion: 1 / 2^(1/3) : 1 : 2^(1/3) ) Module for the container fractal 34 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Container fractal with tubular module 35 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Cantor set (preserves area) Cantor dust in two dimensions Castle fractal, based on the two-dimensional Cantor dust 36 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Pythagorean trees and tiling 37 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Y-fractal, made with a 3-d-printer at the 3D LAB B25, Institute of Geometry, TU Dresden 38 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Branching fractals, 2006 39 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Yuken Teruya, Notice-Forest 2005, cover, detail Yuken Teruya, Notice-Forest 2004, cover, detail 40 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
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.) 41 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
Landscape of Corse with a fictional building 42 / 42 Architectural Fractals – Daniel Lordick, TU Dresden
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