fractal forms

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Fractal Cities - A Geometry of Form and Function

This book presents an initial attempt to apply fractal geometry to cities. In fact, we go beyond this and argue that cities are fractal in form, and that much of our pre-existing urban theory is a theory of the fractal city.

In terms of theory, we show here that the architect’s physical determinism concerning the city can be captured and elaborated in terms of fractals while the geographer’s concern for the economic theory of location is entirely consistent with the use of fractal ideas.

© Michael Batty ©Paul Longley

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Snow is a natural phenomenon. It  consists of the precipitation of small ice crystals with fractal geometrical forms when high concentrations of water vapor accumulates in the atmosphere at temperatures under  0°C. It is only then when snow happens!!!

But one of the most curious and incredible things about this white coat, which you generally see in your back yard during the christmas eve, are the beautiful and perfectly geometrical shapes of the snow crystals. If you take a detailed look to one of this pictures, you are going to notice that every single snow flake has faultless hexagonal geometry, ( each one with six arms) with no exception. Isn’t it amazing? These are master pieces of art of the most perfectionist artist: nature!!!

All the photographs in this post were taken by Russian photographer  Alexey Kljatov, we do not own this material.

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Some time has passed since I posted about a mathematician and I am incredibly happy to come back to this project with such a wonderful person.

Benoit B. Mandelbrot, born on 20th November 1924, was a Polish-born, French and American scientist-mathematician. He has been most widely recognized and honored for his discoveries in the field of fractal geometry.

In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, “Fractals: Form, Chance and Dimension”. According to mathematics scientist Stephen Wolfram, the book was a “breakthrough” for Mandelbrot, who until then would typically “apply fairly straightforward mathematics … to areas that had barely seen the light of serious mathematics before.” Wolfram adds that as a result of this new research, he was no longer a “wandering scientist”, and later called him “the father of fractals”:

<<Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called “fractals”, that are equally “rough” at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.>>