Scale in Fractal Urban Analysis

This is a variation of Mandelbrot's set. It seems to be an Euclidian image, but it is a real fractal. Personal archives.

Aspirin under a microscope. Web download

“De hecho geometría y orden son en más de un caso sinónimos. Para ello basta pensar que así como hay geometrías en plural, con sentidos dialécticos, complementarios y/o antagónicos... también hay niveles de orden en plural y nadie puede fijar frontera exacta entre orden y desorden. Una sociedad humana en tanto grupo constituido sobre la base de un orden de sus interrelaciones implica una geometría de hombres”. (G. Breyer, 2000)

The form is related to our perception and points of view. There are many designs that are strictly Euclidean, but it can happen they end up in fractal versions; an interesting example is the quincunx which represents the "light of Allah", in African and African-American cultures. This religious symbol of five squares, with one in the middle and one at each corner, after several iterations, shows a recursive geometric pattern, so it is a kind of fractal. And sometimes, the fractal is veiled, it will be found in the change of scale, for example, an aspirin is cylindrical in shape, but once under a microscope it looks like a beautiful multicolored fractal.

Quincunx. Liforia.com

The working level system for fractal urban analysis consists of: morphological configurations at a satellite scale that define the edges of expansion and urban sprawl of the city; the region or territory of geographic features, where human activities are interrelated and connected with other regions inside the city; neighborhoods of more specific social interactions between these cultures; groups of settlements (ex. urban blocks) within neighborhoods and a final micro level that takes into account the interference of the human body in the landscape and built environment. A city with real fractal tendencies has fractal components in all scales, from regional scales (satellite) to the microscale of buildings’ materials. This concept unifies planning, urban design and architecture, as different scales in a “ large¨ discipline.
There are two basic ways to study a fractal structure: examining the changes according to variations in scale or maintaining a fixed scale and varying measures. The method can be applied to the study of urban areas and exploration of edges. The resultant for Fractal Dimensions is estimated in the range between 1 and 2.

With regard to the scale, it will be consistent with the criterion of the design process. At the highest level of detail, the morphological analysis will show greater detail in the demarcation of built-up and vacant areas, and vice-versa. That is, in a satellite picture, showing built-up areas, we can separate areas of forestation, constructions, water, land, etc.. But getting closer, it is essential to show dwellings separately, with their courtyards and set backs. The same concept applies to the analysis of urban profiles or groups of facades, texture analysis will be included, if necessary. Once the filtered image is achieved, it should be evaluated whether or not it serves to our purpose. If the result is not convenient for our objective, we will seek another software or another method, accepting that sometimes research is a matter of trial and error. But software can not be wrong in the development of a tool, the error of criterion is simply human.

It is important to understand that cities are not deterministic fractals. In consequence, for different scales, the fractal dimension result will be different. If we are looking for autosimilarity, the process has to be done only in the selected scale, it means, the aerial picture in the background will be the same one in all the iterations. Then, it would be interesting to compare the results for different scales, as I have done below.

Three different scales in Dana Point. The fractal Dimension from left to right is D=1.8753; D=1.9131; D=1.6615

Here is a video, though it is in Spanish, you can easily understand the methodology.