Bohemian Matrices

Fibonacci-Mandelbrot 4...30
A plot in the complex plane of the roots of the Fibonacci-Mandelbrot polynomials $q_0(z) = 0$; q_1(z) = 1$; q_{n+1}(z) = zq_{n}(z)q_{n-1}(z) + 1$ for degrees 4 through 30. The roots are computed as the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix. Color represents the minimum degree Fibonacci-Mandelbrot polynomial the root is a solution of. The plot is viewed on [-2-1.25i, 0.5+1.25i]. Plot produced by Eunice Chan. For more information see: A comparison of solution methods for Mandelbrot-like polynomials.