### Stegreifentwerfen "gesteckt nicht geschraubt 2.0"

digitales Stegreifentwerfen

G. Wurzer, W.E. Lorenz, S. Swoboda. Im Zuge der Lehrveranstaltung wird die Digitalisierung vom Entwurfsprozess bis zur Produktion an Hand einer selbsttragenden Holzstruktur untersucht: vom Stadtmöbel über die Skulptur zur Brücke. ...

### dap – digital architecture and planning

TU Wien | dap – digital architecture and planning

Logo und CI Entwicklung (Logo, Briefpapier, Visitenkarte)

### SimAUD 2020:

Proceedings

2020 Proceedings of the Symposium on Simulation for Architecture and Urban Design

A. Chronis, G. Wurzer, W.E. Lorenz, C.M. Herr, U. Pont, D. Cupkova, G. Wainer (ed.)

SimAUD, Vienna (online), 2020, ISBN: 978-1-56555-371-2; 622 pages

zu den Proceedings

## I. Introduction... Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth ... [01] This quotation by Mandelbrot shows that the Euclidean geometry - the perfect “clinical” shapes of cones, pyramids, cubes and spheres - is not the best way to describe natural objects. Clouds, mountains, coastlines and bark are all in contrast to Euclidean figures not smooth but rugged and they offer the same irregularity in smaller scales, which are some important characteristics of fractals - see chapter “ |

## 1.1 Mandelbrot - Fractals - Theories and Explanations... Fractals will make you see everything differently. ... You risk the loss of your childhood vision of clouds, forests, galaxies, leaves, flowers, rocks, mountains, torrents of water, carpets, bricks, and much else besides [02] The computer-scientist Benoit Mandelbrot introduced the word "fractal" [03] in the year 1975 to describe irregular, not smooth, curves. Fractal geometry in general has become more and more popular since Benoit Mandelbrot’s book “ |

## 1.2 An OverviewWe can describe mountains, clouds, trees and flowers by models consisting of simpler geometric forms based on Euclidean geometry, for example using net models in CAD, but are they exactly what nature is [06] The first two chapters below give an introduction to fractals and fractal geometry in a more general way, listing characteristics and explaining some examples. Then one chapter follows about the differences between Euclidean and fractal geometry and their expressions in the Euclidean and fractal dimension, introducing and explaining some measuring-methods of the fractal dimension. Until a short time ago scientists described nature through so called “smooth” continuous mathematics, which is the mathematics of smooth forms such as lines, curves and planes and which is expressed in the language of Euclidean geometry. The “new” science of complexity [07] does not try to simulate any more the rugged character of nature through smooth forms but it deals with the raggedness of the structure itself - this field of mathematics is expressed in the language of fractal geometry: “The whole is more than its parts”. The fractal new geometric art shows surprising kinship to Grand Master paintings or Beaux Arts architecture. An obvious reason is that classical visual arts, like fractals, involve very many scales of length and favor self-similarity [08]. Chapter “ |

## Footnotes[01] Comparison of natural objects with Euclidean geometry by the mathematician Benoit Mandelbrot in "The Fractal Geometry of Nature". Bovill Carl, Fractal Geometry in Architecture and Design (1996), Birkhäuser Bosten, ISBN 3-7643-3795-8, p.4, Mandelbrot Benoit B., Dr. Zähle Ulrich (editor of the german edition), Die fraktale Geometrie der Natur (1991) einmalige Sonderausgabe, Birkhäuser Verlag Berlin, ISBN 3-7643-2646-8, p.13. |