kleines Entwerfen "gesteckt nicht geschraubt"
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. ...
Visual representation of adjacencies
eCAADe SIGraDi 2019 - Architecture in the Age of the 4th Industrial Revolution. (paper & talk)
W Lorenz, G. Wurzer. This paper is based on the assumption that a key challenge of good design is spatial organisation as a result of functional requirements. The authors present a new NetLogo application that assists designers to understand the proposed functional relationships (of spaces) by visualizing them graphically. ...
kleines Entwerfen customized bricks
G. Wurzer, W.E. Lorenz, S. Swoboda. Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage algorithmisch zu Denken. Durch das Präzisieren der Problemstellung sind die Studierenden in der Lage den sinnvollen Einsatz von Algorithmen im Planungsprozess gedanklich zu erfassen. ...
The box-counting dimension “Db” is equivalent to Mandelbrot's fractal dimension “D”. Generally no clearly repeating self-similar structure as in the Koch curve can be found in any real-world object, which means that these less regular shapes cannot be divided into equal parts and by that the self-similarity dimension method will not work. But there is also a problem when measuring the dimension of a coastline or part of it with the help of the measuring-method if surrounding islands are to be included.
In such cases the so-called box-counting method, which is often used by calculating programs for the computer, takes remedial measures. It works very well for images prepared as a black and white image of any object. At the same time it is important to remember that it is the dimension of the image, which is measured, and not the object itself.
How does the box-counting method work? First a grid is put over the image, e.g. a border line or an elevation of a building. Then the boxes, which contain part of this border or edges of the elevation, are marked. The number of boxes of the bottom row of the grid gives the unite-size, the scale. At the next step a lower grid is chosen and again those boxes, which contain a relevant part of the image, are marked. That means by using the box-counting method not the line is divided into parts but the grid, which is put over the line. For calculation the occupied boxes of each grid-size are counted. Finally, as with the measuring-methods above, different scales are compared, see picture 25. The formula for calculating the fractal dimension is the following:
picture 25: The box-counting method
For better comparison once more the example of the coastline of Britain is used. Again surrounding islands are excluded from the measurement, though the box-counting method can include the surrounding islands in contrast to the measuring-method.
E.g. the box-counting dimension of the coastline of Britain measured in picture 25 between the scale of 1/s2 and 1/s3 amounts to Db=1.31. The calculated measured dimension “d” for the scale between the unit length of 100km and 50 km is 0.308, that is Db=1.308.
Graphically the box-counting dimension is calculated by transforming the results, marked boxes and the unit-sizes, into a log-log graph. The gradient of the resulting line of the log-log graph is the fractal dimension of the image. But as I will mention later in chapter “7 Problems with Measuring” there are some problems to cope with when using programs, which generate the dimension. Mostly the problems result in a non-straight graph-line. That means that there may be some shortcomings in the original box-sizes of the grids or the quality of the image. Therefore a replacement-line has to be calculated which runs straight. This line is the average of all dimensions given by the log-log graph.