algorithmic design of a "Würschtlstand"
W.E. Lorenz, G. Wurzer, S. Swoboda. Ziel dieses Entwerfens ist es, Studierenden das algorithmische Denken näherzubringen und die Fähigkeit zu geben nach dem Präzisieren der Problemstellung den sinnvollen Einsatz von Algorithmen im Planungsprozess gedanklich zu erfassen. ...
Programming for Architects V2019
Anhand von Planungsaufgaben wird ein Grundwissen über die Programmierung vermittelt. Um die Einsatzmöglichkeiten eines selbstgeschriebenen Scripts in Architekturwerkzeugen aufzuzeigen, erfolgt im Speziellen das Erlernen der Syntax von Python und dessen Implementierung in Rhinoceros(R).
Benoit Mandelbrot, the “father” of the popularity of fractals today, introduced fractal geometry by the question of how long the coastline of Britain is. This question of length seems to be very trivial but nevertheless there is more than one possible answer.
picture 01: The coastline of Britain:
How long is the coastline of Britain?
Looking down on the coastline from a great distance, out of an airplane, we will recognize the character of the border on principle - if its rough or smooth -, but we will not see all the small inlets which will come up when we are closer to the coastline, for example when walking along the beach.
Nevertheless there are some limits to this length-measurement. One limit is the size of an atom as a physical border - theoretically, without any limit, the length of the coastline would reach infinity at an infinite small scale because of the infinite number of inlets. The other limit is the correct definition of the coastline, that is where the exact border between water and land is and at which time it should be measured, at high tide or low tide. Consequently, it may then be better to choose a rock of about 20 meters length as the lower limit instead of an atom. This value also arises from the fact that regions of coastlines have been cultivated by man -this has turned them into smoother parts. Therefore, to avoid falsifications, smaller scales have to be excluded from measurement.
Another example of scale-dependence is the length-measurements of borders between countries. The problem of measuring them has been known for a long time and in most cases the deviations do no harm: e.g. the circumstance that the length of the border between Spain and Portugal is given differently by the officials of these two countries has no consequences. The difference results from the fact that the official maps of Spain have a bigger scale than those of Portugal . Here we find the same phenomenon as with the coastline above - the maps of Portugal show more edges and corners, which mean that the border is longer than on the maps of Spain. The length given in the Spanish encyclopedia is 987km and that in the Portuguese one is 1.214 km.
As early as in the year 1961, Lewis Fry Richardson examined the growth rate of the length for different curves such as coastlines and borderlines, by replacing the original curve by a polygon consisting of equal-sized lines - the unit length. For each curve and for a certain he got an overall length through the approximation formula .
As unit-lengths lead to different total-lengths, borders, coastlines and other fractal curves cannot be compared by their length. Firstly, because one "unit-length" for all measurements would have to be defined, which has not been done yet, and secondly, nature also exists without man, which means that a typical man-defined unit-length would place man above nature. Therefore the fractal dimension “D” will be a better parameter for comparison.
Facades often display some kind of roughness - for example let’s think of window-frames, the distribution of windows and doors, the character of bricks and other materials, the structure of the roof and the wall.
 Spain is a larger country than Portugal, which means it would need more maps of the same measuring scale as Portugal to show the whole country. Voß Herbert, Chaos und Fraktale - selbst programmieren (1994), Franzis-Verlag GmbH Österreich, ISBN 3-7723-7003-9, p.13.