Botanical Biomorph Arising from the Iteration of z → z³ + μ

The pattern described here is a biomorph image of the type first described by Pickover [1, 2, 3]. The pattern arises from the iteration of a very simple expression, namely, z → z³ + μ, where μ and z are complex numbers. The image was rendered with the aid of a Julia set algorithm and the special convergence criterion required to reveal biomorphic forms [1]. According to this criterion, z is taken to be convergent and a point is plotted if either the real or the imaginary part of z is small after many iterations…