TY - JOUR
T1 - General Mandelbrot sets and Julia sets with color symmetry from equivariant mappings of the modular group
AU - Chung, K. W.
AU - Chan, H. S Y
AU - Chen, N.
PY - 2000/12
Y1 - 2000/12
N2 - 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.
AB - 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.
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U2 - 10.1016/S0097-8493(00)00093-5
DO - 10.1016/S0097-8493(00)00093-5
M3 - RGC 21 - Publication in refereed journal
SN - 0097-8493
VL - 24
SP - 911
EP - 918
JO - Computers and Graphics (Pergamon)
JF - Computers and Graphics (Pergamon)
IS - 6
ER -