Quasi-Mandelbrot sets for perturbed complex analytic maps: visual patterns

07/10/2008

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by   A. V. Toporensky, et al.

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We consider perturbations of the complex quadratic map z → z^2 +c and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the perturbation reaches some critical value) or continuously. In the latter case we have a smooth transition from the classical form of the set to some forms, constructed from mostly linear structures, as it is typical for two-dimensional real number dynamics. Two examples of continuous evolution of the quasi-Mandelbrot set are described.