Frank Wang

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Beautiful Fractal Patterns in the Roots of Polynomials

  • polynomials
  • root-solving
  • fractals
  • math



This image is a density map of all the complex polynomial roots of four billion polynomials with coefficients in \(\{0, 1, -1\}\). Roots which appear with multiplicity greater than one are plotted only once. It is super high resolution so explore it at your leisure.

The roots are generated using a small python script which was run on a Ryzen 1700 machine for four days. Source code can be found on github.