The Fractal God has Died – We’ll Miss You Benoit Mandelbrot

Benoit Mandelbrot, father of Fractal Geometry, has died at 85.

Mandelbrot was born in Poland in 1924, but grew up in France. Most of his work was done in the United States, and since receiving dual-citizenship has often been referred as a Franco-American, despite Polish background. He has done significant work in mathematical physics and quantitative financing, but he is most famously known for being the “Father of Fractal Geometry”.

Fractals are geometric shape that when split into parts or zoomed-in on, it retains an approximate copy of the whole(at a reduced size), a property known as self-similarity. They’re one of the most beautiful shapes, and occur often in nature. It’s properties are as follows (taken directly from

A fractal often has the following features:

  • It has a fine structure at arbitrarily small scales.
  • It is too irregular to be easily described in traditional Euclidean geometric language.
  • It is self-similar (at least approximately or stochastically).
  • It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
  • It has a simple and recursive definition.
 Fractal Geometry in a piece of romanesco broccoli
Fractals have many applications. They can be used to create music through algorithmic composition, seen in the practice of Seismology, used to create environments in video games much easier, image compression, helps to classify Histopathology in medicine, as well as many others.
Example of the infinite nature of Fractals
 There are three classifications of Fractals, exact self-similarity, quasi self-similarity, and statistical self-similarity. All with varying degrees of similarity strength.
It’s a shame that Mandelbrot has left us, but he lived a good long life. I’m sure if an afterlife exists, he’s riding the wave of a fractal as we speak.

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