Generalized Julia Sets: from Cantor Bouquet to Cantor Cheese

Year: 2019 Authors: Stefanie Hittmeyer; Bernd Krauskopf; Hinke M. Osinga

Core claim

The map f_λ(z) = (1 - λ + λ|z|^2)(z/|z|)^2 + c creates generalized Julia sets whose geometry is governed by infinitely many critical values on a circle.

Topics

Julia sets, complex dynamics, fractal geometry, aesthetic rendering

Domains

dynamical systems, complex quadratic family, non-analytic perturbation, iterated maps, mathematical art, aesthetic image generation, fractal visualization

Methods

orbit iteration, escape-time coloring, parameter sweep, polar-coordinate analysis

Media

computer-generated images, color-coded complex-plane grids, fractal renderings

Source status

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