Chaotic Attractors Near Forbidden Symmetry
نویسندگان
چکیده
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 structure. Like Penrose tilings and diffraction patterns of quasicrystals, our constructions include local rotations that are forbidden from being global by classical crystallographic theory.
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 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 کاملSymmetry-increasing Bifurcation of Chaotic Attractors
Bifurcation in symmetric systems is typically associated with spontaneous symmetry breaking. That is, bifurcation is associated with new solutions having less symmetry. In this paper we show that symmetry-increasing bifurcation in the discrete dynamics of symmetric mappings is possible (and is perhaps generic). The reason for these bifurcations may be understood as follows. The existence of one...
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 کاملPeeling bifurcations of toroidal chaotic attractors.
Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the ...
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 2008