Methods used to compute it include various embarassingly parallel implementations, the Hubbard-Douady potential, and the Milnor algorithm.
Methods used to compute it include various embarassingly parallel implementations, the Hubbard-Douady potential, and the Milnor algorithm. It is self-similar, as well as being connected and compact. One definition of this construction is as the connectedness locus of a family of complex polynomials, f sub c of z. The more common definition shows it as the set of all complex points c such that the sequence zero, f sub c of zero, f sub c of f sub c of zero, et cetera stays within a ring of finite radius around the origin, where f sub c of z is the polynomial z squared ►plus c. FTP, identify this set, best known as a fractal cardioid with bulbs and "seahorse"-like shapes.
Methods used to compute it include various embarassingly parallel implementations, the Hubbard-Douady potential, and the Milnor algorithm.
Mandelbrot set