### Visual representation of adjacencies

eCAADe SIGraDi 2019 - Architecture in the Age of the 4th Industrial Revolution. (paper & talk)

W Lorenz, G. Wurzer. This paper is based on the assumption that a key challenge of good design is spatial organisation as a result of functional requirements. The authors present a new NetLogo application that assists designers to understand the proposed functional relationships (of spaces) by visualizing them graphically. ...

### kleines Entwerfen customized bricks

digitales Entwerfen

G. Wurzer, W.E. Lorenz, S. Swoboda. Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage algorithmisch zu Denken. Durch das Präzisieren der Problemstellung sind die Studierenden in der Lage den sinnvollen Einsatz von Algorithmen im Planungsprozess gedanklich zu erfassen. ...

### Bridgemagazine Webpage

Webdesign für das bridgmagazin – Medieninhaber (Herausgeber) und Verleger: Österreichischer Bridgesportverband (ÖBV) | Audio Video Werbe-GmbH.

### Stegreifentwerfen Hot Wood follow up

follow up "Würschtlstand"

W.E. Lorenz, G. Wurzer, S. Swoboda. Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage algorithmisch zu Denken. Konkret erlangen sie die Fähigkeit jene Teile des Entwurfsprozesses zu erkennen, die ausprogrammiert zu schnelleren und allenfalls besseren Lösungen führen. Dabei greifen die Studierenden auf die Ergebnisse des kleinen Entwerfens "Hot Wood" aus dem Sommersemester 2019 zurück. ...

## 3.2 Chaotic FractalsAnother category of fractals represents the so-called chaotic, non-linear fractals. This fractal type is connected with the theory of chaos, and its elements are obtained by a simple mathematical equation[01] .For visualizing them, each point on the paper or screen is related to a certain number - e.g. in the case of the “Mandelbrot set” this is a complex number. This number is then iterated, that means it is used in a formula and the new number resulting from that is then again used in the same formula, which leads to the next iteration. This sequence of operations is "similar" to the work of the "copy-machine" of linear fractals - with regard to insertion. The insertion is repeated until the numerical values approach infinity, converge or fluctuate between several numbers. Depending on the result, the original point may be colored differently. |

## 3.2.1 The Mandelbrot SetThe Mandelbrot-fractal itself is the picture of the Mandelbrot set - the Mandelbrot set being the numerical set of the complex numbers for that is valid if, being repeatedly put into the formula , the absolute value remains a finite number[02] . The plane in which it is drawn is called the complex plane where each point represents a complex number of the form For visualizing the set, each pixel of the screen, representing a certain complex number, is iterated in the formula . For each pixel, point, , mostly fixed in the zero point , remains the same but the value of “ |

picture 14: Mandelbrot set and Julia sets On the left side the sequence of , named “orbit”, is shown for three different starting points “ |

## 3.2.2 The Julia SetsThe Julia sets use the same formula as for the Mandelbrot set, whereas this time for one certain Julia set, the value of “ For each value of “ How can it be proved easily that a certain set is not interrupted? Gaston Julia found out that one only has to analyze the behavior of the critical zero-point, . The resulting picture of “ |

## Footnotes[01] Jürgens Hartmut, Peitgen Heinz-Otto, Saupe Dietmar: Fraktale - eine neue Sprache für komplexe Strukturen, Spektrum der Wissenschaft (9/1989), p.59. |