General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group

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Original languageEnglish
Pages (from-to)911-918
Journal / PublicationComputers and Graphics (Pergamon)
Issue number6
Publication statusPublished - Dec 2000


A method for constructing the general M (Mandelbrot) set of a non-analytic mapping is presented. The equivariant mapping with symmetry of the modular group is considered as an illustration. By investigating the distribution of attractors in the upper half-plane and the assignment of colors to each attractor, an algorithm is presented for the construction of filled-in Julia sets with 2- or 3-color symmetry. Such Julia sets not only reveal the characteristics of a system, but also have high artistic appeal.