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- W3022757445 abstract "Attractors arising from the iteration of functions in the plane that are designed to have symmetry have been the subject of recent study. These attractors can be forced to have n-fold rotational symmetry and reflections can be forced or avoided. Examples of attractors with forced symmetry in three and higher dimensions have been constructed in this chapter. The chapter describes the creation of attractors in three spaces that are forced to have different symmetries in different regions. These attractors are then projected to the plane using a semi-inverted central projection that results in placing the attractor inside an annulus––where one edge of the attractor has one symmetry type and the other edge has a different symmetry type. Two functions of the plane having distinct symmetries are intertwined using a sinew function to create a function of three variables having different symmetries in different regions of space. The attractor resulting from the iteration of this function can be visualized using a nonlinear semi-inverted projection to the plane. This projection makes the dueling symmetries of the attractor apparent. Schemes similar to genetic algorithms can be used to search parameter space for interesting examples of attractors with these dueling symmetries." @default.
- W3022757445 created "2020-05-13" @default.
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- W3022757445 date "1998-01-01" @default.
- W3022757445 modified "2023-09-26" @default.
- W3022757445 title "Attractors with dueling symmetry" @default.
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- W3022757445 doi "https://doi.org/10.1016/b978-044450002-1/50013-8" @default.
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