Saturday, March 1, 2008

Fractals in flowers and fields


Consider what this picture has in common with the next two.

"The term ‘fractal’ (from the Latin fractus, meaning ‘broken’), introduced by Benoit Mandelbrot about
25 years ago, is used to characterize spatial and/or temporal phenomena that are continuous but not
differentiable. Geometrically, a fractal is a rough or fragmented geometric shape that can be subdivided
into parts, each of which is (at least approximately) a reduced-size copy of the whole...
"Fractal properties include self-similarity or affinity, scale symmetry, scale independence or invariance,
heterogeneity, complexity, and infinite length or detail...
"Fractal theory offers methods for describing the inherent irregularity of natural objects. In fractal analysis, the Euclidean concept of ‘length’ is viewed as a process. This process is characterized by a constant parameter D known as the fractal (or fractional) dimension."

Li, Bai-Lian. 2002. "Fractal dimensions"in Encyclopedia of Environmetrics. Abdel H. El-Shaarawi and Walter W. Piegorsch, eds. John Wiley & Sons, Ltd, Chichester,Volume 2, pp 821–825

These are concepts that I'm learning and just beginning to understand. Heterogeneity here appears somewhat self-similar, although ecological patterns are often actually scale co-variant. For your consideration.

Next post will not include more flowers, I promise!

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