Computer Visualization of Julia Sets for Maps beyond Complex Analyticity

Abstract

Using the computer program creating Julia sets for two-dimensional maps we have made computer animation showing how Julia sets for the Peckham map alters when the parameter of the map is changing. The Peckham map is a one-parameter map which includes the complex map z=z^2+c, and is nonanalytical for other values of the parameter. Computer animation of Julia fractal sets allows seeing how patterns typical for complex maps gradually destroy.