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)

picnic table

File format: Grasshopper® for Rhinoceros® 5 ... link 

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. ...

II Fractals - A Definition

The best way to define a fractal is through its attributes: a fractal is "rugged", which means that it is nowhere smooth, it is "self-similar", which means that parts look like the whole, it is "developed through iterations", which means that a transformation is repeatedly applied and it is "dependent on the starting conditions". Another characteristic is that a fractal is "complex", but nevertheless it can be described by simple algorithms - that also means that beneath most natural rugged objects there is some order.

2.1 What is a Fractal?

"Fractals are objects of any kind whose spatial form is nowhere smooth, hence termed "irregular", and whose irregularity repeats itself geometrically across many scales"[01].

In fact there are so many different types of fractals, some of which will be introduced in chapter "3 Different Fractals", that it is not possible to give one definition for all of them. Besides, when we are talking about fractals in general we should never forget that there are many which have not been found yet. Considering this circumstance, it is more useful to describe some of their characteristics.

2.2 Characteristics

... the world is chaotic, discontinuous, irregular in its superficial physical form but ... beneath this first impression lies an order which is regular, unyielding and of infinite complexity[02].

2.3 Influences

There is one important fact about the group of "general" fractals namely the natural development. This means that for the growth of natural but also for artificial objects many additional influences have to be thought of. Thus a tree or a fern can be produced by fractal geometry but these pictures nevertheless offer some differences in respect to their natural brothers. A tree standing alone on a hill for example is influenced by the wind blowing there, which forms the tree in one typical form: branches are only to be found on the side turning away from the direction the wind blows. Other influences may be soil and water conditions, kinds of plants nearby and animals.

Nevertheless "true" fractals can produce typical natural and man-made forms, but only under sterile conditions. If some random factor is added then the resulting objects come nearer to the "real" world. Likewise the development of cities underlies a couple of influences like natural barriers such as hills and rivers, but also man-made ones such as roads leading to other towns, important industrial areas and green-zones of which the growth of the city reacts. The same is true for elevations and even ground plans of buildings that react to the surrounding no matter whether it is man-made or natural.

From that follows that if we know the underlying algorithm of any object - under sterile conditions - and if some mechanisms for simulation of certain influences are added, we may determine future developments of e.g. the growth of a city.

Footnotes

[01] Batty and Longley, Fractal Cities (1994), Academic Press Inc., ISBN 0-12-4555-70-5, p.3.
[02] Fractals can be called the geometry of chaos. Batty and Longley, Fractal Cities (1994), Academic Press Inc., ISBN 0-12-4555-70-5, introduction p.v.