Why it is important to compute centers of hyperbolic components of Mandelbrot set?

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The problem of computing centers of hyperbolic components of Mandelbrot set is a polynomial root-finding problem. It is also one of the test problems for polynomial root-finding solvers such as MPSolve. My question is why it is important to compute these points, especially for high orders?

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It is :

  • time consuming task
  • with infinite complexity ( number of centers and periods have no limits) so it can be used as a benchmark for
  • computers
  • programs / algorithms / arbitrary precision libraries