A plot in the complex plane of the roots of the Mandelbrot polynomials $p_0(z) = 0$; $p_{n+1} = zp_{n}^{2}(z) + 1$ for degrees 3 through 19. The roots are computed as the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix. Color represents the minimum degree 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.
