Stegreifentwerfen "gesteckt nicht geschraubt 2.0"
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
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Logo und CI Entwicklung (Logo, Briefpapier, Visitenkarte)
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
2.2.3 Characteristics - A Fractal is Infinitely Complex
Fractals are highly complex, that means zooming in will bring up more and more details of the object, a characteristic that continues until infinity.
Chaotic fractals: Already in the 20ies of the 20th century the French mathematicians Gaston Julia and Pierre Fatou concerned themselves with the question of fractal geometry. Both examined what would happen to a point “Z” of the complex number-plane if the transformation was repeatedly applied to it . Gaston Julia discovered that calculating the function repeatedly might deliver unforeseen “chaotically” results.
For further information about Julia sets and the Mandelbrot set see chapter “3.2 Chaotic Fractals”.
picture 07: The Mandelbrot set
The Mandelbrot set, the black middle heart-shaped object, is a unit and nowhere interrupted. That means looking at the border areas there seem to be isolated islands, black colored points. But coming closer to this marginal zone, we will find "streets" and "places" through which other fields of the Mandelbrot set are connected. This area is very interesting because zooming deeper into it always means getting new information about the set and finding forms that are similar to each other.
 Gaston Julia like his rival Pierre Fatou analyzed the phenomenon of feedback. They realized the influence of the constant “C” but they did not have the possibility of computers to generate pictures of its behavior. In simple cases points near the zero point converge to a certain point - fixed-point of f(z) -, while outer points approach infinity. In between those two areas there is an infinitely small border that is today called Julia set. Points of the two areas tend to stay away from this infinitesimal border, to outer or inner areas. Jürgens Hartmut, Peitgen Heinz-Otto, Saupe Dietmar: Fraktale - eine neue Sprache für komplexe Strukturen, Spektrum der Wissenschaft (9/1989), p.59