Urban Exercises With Fractal Spectrum

Fractal Wave. By Myriam Mahiques

The topic of “time” has been very difficult to analyze in the visual arts, for the lack of representational means to describe the dynamics of the reality. The problem has been investigated and developed by the artists of Cubism and Futurism, and in architecture, the Bauhaus developed its projects to be seen and experienced from different points of view. The fact is that the conventional representations of the architecture and urbanism lack possibilities to communicate temporary dimensions. This situation is irreversibly changing thanks to the incorporation of electronic simulations, with its summit settled down in the virtual reality. In consequence, our attention on the architectural object in itself and the city, will be overturned toward how we experience them. It is a re-conceptualization of the architectural design as design of architectural multi-sensorial experiences.

I offer an approach to the problematic previously described, by means of the use of an innovative mensuration tool -fractal spectrum- that I have achieved with the software HarFA 5.3, created by the Czech professors Oldrich Zmeskal, Tomas Bzatek, Martín Hezadal and Miroslav Buchnicek, from the Faculty of Chemistry, Institute of Physical and Applied Chemistry, Brno. University of Technology.

The fractal spectrum is used when the image to analyze is ambiguous, for instance, an enlarged picture of part of a printed letter in a newspaper. If we want to analyze this type of image, formally not defined, that shows two diffuse color sectors, at first we would not know which part of the color information would be masked (filtered) to form the corresponding fractal. To resolve this issue, all the possible fractals should be formed, to determine the fractal dimension and examine the successive results as a function of the masking conditions. This represents a fractal spectrum. Each point of data in the graph of coordinates is colored according to its specific information (intensity, red, green, and blue channels).

The example cited above is elementary. Advancing in the analytic complexity, these directional studies are also applied to obtain the spectra of sea waves. The spectrum models are described like empiric expressions of adjustments derived of experimental data: the empiric data usually show that the fractal nature of several phenomena is often different in scaling. Beginning with a definition of a fractal model of the surface of the sea, the function of spatial auto-correlation (in simpler terms, autocorrelation is achieved with the automatic application of filters) is calculated based on a Fourier transform in two dimensions. Then, it is theoretically demonstrated how the curve in the graph of coordinates, to reach a balance range, depends on the fractal dimension of the surface of the sea. (See Berizzi F, Dalle Mese E. En IEE proceedings. Radar, sonar and navigation. Vol 148, No 2, pp. 56-66. 2001). Another application is the multi-scalar analysis in thermodynamics.

First sequence of urban growth simulation with Fractal spectrum. All pictures and exercises by Myriam B. Mahiques

Second sequence

Third sequence

Fourth sequence.

I have found that this function, applied to urban morphology based on random fractals, helps us to make the morphological analysis extensive through time, from the first forms (in fact first settlements) to an extremely compact agglomerate. The software goes opening up and closing the urban fabric maintaining the same pattern, and at the same time the graph of coordinates goes changing continually in consequence . The colors, as it was explained, correspond to the areas under analysis and also to a combination among them.