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Description

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line…"

— Benoît Mandelbrot, The Fractal Geometry of Nature, 1982

In nature, there are also "pure" forms known as crystals. My mathematical research over the past 20 years shows that the Mandelbrot algorithm can also be used to describe this important aspect of nature. In fact, the tricomplex Mandelbrot set contains, as 3D slices, the cube, the octahedron and the tetrahedron.

In this illustration, I have combined these three Platonic solids with pyrite, fluoride, and sphalerite. For more information on this relationship between the Platonic solids and the Mandelbrot set, you are welcome to consult a lecture given in Rome in 2018.

www.3dfractals.com/docs/Chaos_…

Photo by Dominic Rochon (Metafractals), 2021

Description

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line…"

— Benoît Mandelbrot, The Fractal Geometry of Nature, 1982

In nature, there are also "pure" forms known as crystals. My mathematical research over the past 20 years shows that the Mandelbrot algorithm can also be used to describe this important aspect of nature. In fact, the tricomplex Mandelbrot set contains, as 3D slices, the cube, the octahedron and the tetrahedron.

In this illustration, I have combined these three Platonic solids with pyrite, fluoride, and sphalerite. For more information on this relationship between the Platonic solids and the Mandelbrot set, you are welcome to consult a lecture given in Rome in 2018.

www.3dfractals.com/docs/Chaos_…

Photo by Dominic Rochon (Metafractals), 2021