Automatic Generation of Chaotic Attractors with Various Cyclic or Dihe- dral Symmetries
نویسندگان
چکیده
Chaotic attractors are created by iterating functions that are equivariant with respect to the cyclic or dihedral groups. An improved color scheme based on the visit frequency of the pixels is proposed to render chaotic attractors. By normalization and scale transformation, aesthetic patterns which simultaneously have several kinds of cyclic or dihedral symmetries are generated. This method can be used to yield a great number of aesthetic patterns automatically.
منابع مشابه
Chaotic attractors with cyclic symmetry revisited
Chaotic attractors generated by the iteration of polynomial functions with cyclic symmetry have been the subject of recent study. A new formulation is investigated which generates cyclic symmetry using arbitrary functions. This allows the use of diverse function classes including functions with various types of singularities. The resulting images have significantly more diversity than those ari...
متن کاملChaotic Attractors Near Forbidden Symmetry
We explore chaotic attractors with symmetries that are close to forbidden symmetries. In particular, attractors with planar crystallographic symmetry that contain an imperfect, but apparent, rotation that does not preserve the lattice of translations are constructed. This gives us a visual representation of patterns which have low symmetry type, but which contain additional, provocative structu...
متن کاملSymmetry Groups of Attractors
For maps equivariant under the action of a nite group ? on R n , the possible symmetries of xed points are known and correspond to the isotropy subgroups. This paper investigates the possible symmetries of arbitrary, possibly chaotic, attractors and nds that the necessary conditions of Melbourne, Dellnitz and Golubitsky 15] are also suucient, at least for continuous maps. The result shows that ...
متن کاملChaotic attractors and evolving planar symmetry
Building upon work which illustrated families of chaotic functions with planar symmetries, we explore evolving attractors from one symmetry type to another. We observe different ways the symmetries evolve and pay attention to those which exhibit degenerate behavior. Visually attractive images with low symmetry can be created in this way.
متن کاملChaotic intermittency of patterns in symmetric systems
We examine some properties of attractors for symmetric dynamical systems that show what we refer to as`chaotic intermittency'. These are attractors that contain points with several diierent symmetry types, with the consequence that attracted trajectories come arbitrarily close to possessing a variety of diierent symmetries. Such attractors include heteroclinic attractors, on-oo and in-out inter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015