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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).
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5.1.1 Changing of DimensionsBenoit Mandelbrot used a woolskein to show the changing of mathematical constancy  the changing of the "effective" dimensions. For a viewer who is far enough away from the woolskein, which may have a diameter of 10 centimeters and consists of a 1millimeter yarn, it looks like a point, a zerodimensional object. In a 10 centimeter resolution the skein is a threedimensional object, in a 10 millimeter resolution it turns out to be a confusion of onedimensional twines, at a 0.1 millimeter resolution each twine is experienced as a threedimensional column and at a 0.01 millimeter resolution each column turns again into onedimensional fibers. If we zoom in deeper on the resolution of an atom, the woolskein is presented as an object of finite numbers of atomlike points and therefore it is again zerodimensional  remember the Cantor Set. So the woolskein shows a sequence of different effective dimensions. Some badly defined changeover between zones of well defined dimensions are interpreted as fractal zones where the fractal dimension is higher than the topological one[01]. Benoit Mandelbrot also wrote about the surface of timber being spongy but nevertheless the beam is said to be even. This is because of the scale, in a certain ratio of size the regular and continual aspect can describe an object in a correct way. He compared this scale with a tinfoil that is put over a sponge, which follows the surface but does not show the many little complex details, see picture 26[02]. 
picture 26: Bark 
5.1.2 The ScaleRange of a WallObserving a straight wall, built of stones of a certain thickness, height and length from a great distance, the object may look like a straight line  e.g. having a look at the Great Wall of China from the universe it will be identified as a long curve with no width and no height. But coming closer the curve turns into a twodimensional plate with a certain height and length but no width. Finally standing on the wall it will turn out to be a threedimensional object. Then looking at a small stone as part of the wall a couple of meters away, this stone may be experienced as a zerodimensional point. But coming closer once more, this stone turns into a threedimensional object. This changing of dimension can be repeated down to the scale of the atom, which offers a physical border, see picture 27. 
picture 27: Great Wall 
5.1.3 The ScaleRange of an ElevationThe changing of the "effective" dimension is also true for other man made objects. E.g. observing a building from far away it may seem to be a point or, thinking of rows of houses, maybe a line. Coming closer the twodimensional outline can be recognized but no deepness of the elevation. Windows seem to be points and lines. When analyzing the elevation from the front it cannot even be said if it is only a stageprop. Coming closer up to a couple of meters away from the building, more and more details like cuts of the windows and the jumping forward and back of elements of the facade come to one’s attention. On this scale the house is experienced as a threedimensional object. At some point even the roughness and structure of the facade can be felt; it, however, depends on the material of the surface of the building at which distance this will be. In front of the door some more details like the doorknob can be found, which may have looked like a straight line before[03]. Using Euclidean vocabulary implies a certain abstraction such as a plastering facade is actually rugged but is mostly called smooth. This abstraction is taken from a certain scale, a certain measuring: the man and the human body. From a certain distance the facade really looks like the Euclidean flat plane, though thinking of a brick wall, there is always a structure to be observed. This leads to the conclusion that the cut out windows and doors, beside other details such as the structures of walls and door knobs, are what the facade differ from Euclidean shapes at this scale, which is also true for smooth concrete facades. Therefore the straight smooth modern style buildings are also fractal forms on closer observation. At the next stage, when entering the house, the next level of the object is examined. There is a difference between smooth rectangular buildings and a building of differentiated ground plans and elevations. It is easy to take up the first type at once and explain its rooms with a few words. In contrast to that, a “differentiated” house with different heights, different materials has more underlying information to offer. But if there is too much that we cannot understand in the context this can lead to an oversupply of information like in a language we do not understand. In this case the complexity turns into confusion. 
5.1.4 Conclusion“Architectural composition is concerned with the progression of interesting forms from the distant view of the facade to the intimate detail. This progression is necessary to maintain interest”.[04] The principle of stepping forward of details by zooming, which is mostly found in nature, should be taken up as a reflection of the intention of the composition from the whole to the detail. This means that for example a round surface asks for round floor plans, which also means that the resulting concept is understandable from the whole to the detail. The scaling range of an object, and depending on that the gridsize for the boxcounting method, is related to the nature of visual perception. Very fine details can be observed only within a range of two degrees from the center of the inspected object. But significant details are also realized from an angle of 10, 15 and 20 degrees  see picture 28. Each scale has a certain distance to the observed object, which can be expressed by the equation: the distance from the building multiplied by tangent of the angle is equal to the measuring unit size. But there is a difference whether one concentrates on a certain detail or on the whole from the same distance. In the first case, looking at the detail, e.g. a short line in an abstract painting or the doorknob of the entrance, objects around it will also come to our attention. If we concentrate on a larger detail or the whole, e.g. the elevation of the building, smaller details run out of perception[06]. 
picture 28: Vision 1. "Field of vision": that is the region, which can be overlooked without moving one’s eyes.[Fuhrmann Peter, Bauplanung und Bauentwurf: Grundlagen und Methoden der Gebäudelehre (1998), W. Kohlhammer GmbH Stuttgart, p.102.] 
2. "Region of very sharp perception": The picture below shows a diagram of the location of rod and cone cells in the human eye, taken from "Fractal Geometry in Architecture and Design" by Carl Bovill.[09] Details are perceived in the middle part, the fovea and macula. While fine details are only observable within 2 degrees  i.e. a sight cone with an opening angle of 1° , significant details can also be observed through 10, 15 and 20 degrees. 
The range of scales  boxsizes, measuring unit size  that is used for the boxcounting method can be determined by these angles and the distance from the building by: distance from the building * tg a = measuring unit size 

3. "Reading field": This is the region of smallest possible detailperception  within a sight cone with an opening angle of 0°1’. It is derived from the resolving power of the eye and determines the minimum size of details that can be viewed from a certain distance under the prerequisite of sufficient lighting. size of detail > distance * tg 0°1’ example: d=800cm 
Footnotes[01] Mandelbrot Benoit B., Dr. Zähle Ulrich (editor of the German edition), Die fraktale Geometrie der Natur (1991) einmalige Sonderausgabe, Birkhäuser Verlag Berlin, ISBN 3764326468, p.29. 