Benoit Mandelbrot and Fractal Geometry

October 24, 2010


Photographer: Martin Richard
SummaryAuthor: Martin Richard; Jim Foster

The line of a coast. The meandering of a river. The silhouette of a mountain-scape. The branching of trunk to twigs, of artery to capillaries, of the trachea to alveoli, of the forks of lightning. Famed mathematician, Benoit Mandelbrot who died last week at 85, illuminated them all. Mandelbrot coined the term “fractal” to describe the geometry he named, explored and inspired others to explore. He was convinced, and convincing in his argument, that he was describing the geometry of nature. Others, inspired by him, have applied his geometry to the arts, and not only in graphic design but also in music. For example, Heitor Villa Lobos is said to have written melodies based on the rise and fall of the mountains. The concepts of nonlinearity, scale invariance, self-similarity generate many of the endless forms we all admire. Fractal geometry underlies not only the physical forms of nature but the geometry of evolution; the tree of life is itself a fractal.

Image details: The center of the triptych started as a backlit leaf. I reduced it to its fractal structure. The outside frames are flames, on which I superimposed a selection from the Madelbrot set, an iconic image, literally infinite in depth and scope.

About the music:. Years ago, I found “Gingerbread,” by Phil Thomson. I used it to compose this midi, “Son of Sonata,” offered now as my small tribute to my favorite mathematician.