### eCAADe 2020:

Proceedings

FRACAM: A 2.5D Fractal Analysis Method for Facades; Test Environment for a Cell Phone Application to Measure Box Counting Dimension

**Talk and Proceeding**: eCAADe 2020 - RAnthropologic – Architecture and Fabrication in the cognitive age (Berlin, Germany, 2020 | virtual conference) FRACAM: A 2.5D Fractal Analysis Method for Facades

W Lorenz, G. Wurzer

eCAADe-conference, Berlin, Germany (virtual conference), 2020,

presentation (video)

### CAADRIA 2020:

Proceedings

FLÄVIZ in the rezoning process: A Web Application to visualize alternatives of land-use planning

**Talk and Proceeding**: CAADRIA 2020 - RE: Anthropocene, Design in the Age of Humans (Chulalongkorn University, Bangkok, Thailand, 2020 | virtual conference) FLÄVIZ in the rezoning process: A Web Application to visualize alternatives of land-use planning

W Lorenz, G. Wurzer

CAADRIA-conference, Bangkok, Thailand (virtual conference), 2020,

presentation (video)

### USA Chicago Exkursion 2019

Japan Exkursion 02.07.-17.07.2019 (book) W.E. Lorenz, A. Faller (Hrsg.). Mit Beiträgen der Teilnehmerinnen und Teilnehmer der Exkursion nach "Chicago" (2019).

ISBN: 978-3-9504464-2-5

Das Buch beschreibt in einzelnen Kapiteln die vom Institut Architekturwissenschaften, Digitale Architektur und Raumplanung, organisierte Exkursion nach Chicago aus dem Jahr 2019. ...

### 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. ...

## 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. |