Rural settlement of Nahalal in Palestine founded in 1921, shows a restricted growth. Published in National Geographic, february 2008, page 33. On the right side, its corresponding Fourier Transform.
First of all, a warning. We must not be tempted for the beauty of fractals, the intention in my exercise is to find the hidden pattern of a fractal urban simulation, originated in the Jewish rural settlement of Nahalal. Alan Mairson, author of the text accompanying the picture in National Geographic, says the settlement´s shape is rigid, with limited growth. The concept of this center with rays is a reflex of egalitarianism: the circle allows everybody to have equal access to neighbors and facilities.The center contains public buildings surrounded by a residential ring, the farms are beyond and around. When the cooperativist spirit was dissipated in the 90´s, the urban shape was not so strict any more. "The village layout in Nahalal, devised by architect Richard Kauffman, became the pattern for many of the moshavim established before 1948; it is based on concentric circles, with the public buildings (school, administrative and cultural offices, cooperative shops and warehouses) in the center, the homesteads in the innermost circle, the farm buildings in the next, and beyond those, ever-widening circles of gardens and fields. initially to 80 equal parts, 75 parts to the members and 5 parts for the agricultural school (the first two parts and the last three parts contain the agricultural school). This equal parcelling of the land became the trademark geometric shape of Nahalal." (Excerpt from Wikipedia.org)Newton fractals are helpful for simulations of growth for urban morphologies with this particular pattern. To find an analogical Newton fractal is not enough, we still need to find hidden patterns consistent with urban simulations.
Here we have two analogical fractals originated in generalized Newton´s fractals. On the right side, the hidden structure is shown in the FFT image (Fourier Transform).
We have found the rays and the center; The first fractal is a representation of a growing center, the avenues are still empty, they can be associated to freeways. The second fractal is showing the loss of egalitarianism, the urban fabric is extended between the rays, in a chaotic pattern.
The next step is to analyze the Fourier Transform image, to take a decision about the best simulation of urban growth.
On the left, the binary image of the first FFT is shown. On the right, I show a binary image of the second FFT with the chaotic pattern. Definitely, the second image is more accurate for Alan Mairson's explanation. The pattern of rays is lost, as it will be in the future, if farms were mixed with residential use. But the main center, origin of the primary idea is still kept.
Nahalal between 1939 and 1945. Picture by Frank Hurley. http://nla.gov.au/nla.pic-an23565289
All simulation images by Myriam B. Mahiques