Self-Similarity

'Fractal Poetics': A rose is a leaf is a rose is a leaf

Iconic image of Romanesco broccoli, courtesy of Wired.
Iconic image of Romanesco broccoli, courtesy of Wired.

Before Benoit Mandelbrot’s fractal mathematics and Gertrude Stein’s roses, Johann Wolfgang von Goethe wrote about a primal plant, “Urpflanze,” which was constructed as a leaf within a leaf within a leaf. I wonder if his Platonic vision for this plant, from which all other plants derived, was an early imagining of fractal mathematics and response to fractal forms in the natural world (coast lines, human migration patterns, Romanesco broccoli). Visual depictions of fractals have no beginnings or endings in time, no inside or outside in space, and self-similarity and repetition occur at all discernible scales. To my eye, these aspects of visual fractals are pleasing. I am also dissatisfied by the undeviating periodicity of fractals.

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