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. ...

3.5 L-Systems - Lindenmayer-Systems

Lindenmayer-Systems, are like the IFS very close to naturally looking objects. The biologist Aristid Lindenmayer developed this variant to describe plant-forms. Similarly to the transformation rules of IFS, which makes “n” new elements out of one by a certain rule, the Lindenmayer-System in its first step uses symbols as a set of rules. To illustrate this stage, a set of transformations may for example be given by: "l" is replaced by "l+l--l+l".

That means starting with "l", the first iteration for this example runs as follows "l+l--l+l", the second one "(l+l--l+l) + (l+l--l+l) - - (l+l--l+l) + (l+l--l+l)" and so on. But this does not lead to any picture - e.g. plant-form. Therefore a second step is required, which translates the symbols into drawing rules. "l" for example symbolizes a piece of a straight line forward, "-" an angle of e.g. 60 degrees to the right and "+" an angle of 60 degrees to the left. By that it is possible to generate self-similar mathematical fractals but also plants, bushes and trees - see picture 19.

picture 19: Lindenmayer-Systems; the Koch curve:

rule = “l + l - - l + l” with
l = line 
+ = +60 degrees
- = -60 degrees
pictures after 1 and 4 iterations

picture 19: L-Systems; a bush:

rule = “l [ + l ] l [ - l] l” [Jürgens Hartmut, Peitgen Heinz-Otto, Saupe Dietmar: Fraktale - eine neue Sprache für komplexe Strukturen, Spektrum der Wissenschaft (9/1989), p.62.] with
l = line 
+ = +28.58 degrees
- = -28.58 degrees
[ = start of a branch
] = end of a branch
pictures after 1,2 and 4 iterations

picture 19: some more pictures produced with L-Systems

An example for a bush is given in "Scientific American"[01] with "l" being turned into the expression "l [ + l ] l [ - l] l". There "l" once more symbolizes a piece of a straight line forward, "-" a certain angle to the right and "+" one to the left. The new symbol of "[" defines the start and "]" the end of a new branch - see picture 19. The Lindenmayer-System reduces the high information of plants through short instructions, which leads to one possibility of application, the usage in computer-generated film sequences, where computer power has to be reduced.

Footnotes

[01] Jürgens Hartmut, Peitgen Heinz-Otto, Saupe Dietmar: Fraktale - eine neue Sprache für komplexe Strukturen, Spektrum der Wissenschaft (9/1989), p.62.