Research On Methods Of Creation Of Symmetric Images And Construction Of Symmetric Fractal

Symmetric chaos and fractal research has been an important part of nonlinear dynamic systems and graphical research work.There are mainly three types of planar symmetrical chaos and fractal graphics which are symmetrical icons,quilt and symmetrical fractal symmetry.To generate a symmetric icon usually needs a polynomial formula as iterated function,then go through the process of continuous iterative and remove transient can get graphics;Symmetric quilt generation can use a planar trigonometric map,through the process of continuous iterative and remove transient get graphics;Generation of symmetrical fractal is to construct a set of methods have symmetrical compression function system of affine maps.Randomly pick up a different mapping functions according to the probability in iteration process then get symmetry.Symmetric Chaos and Fractal research has been ultimately expanded in two directions:1.Construct symmetric dynamical system in 2D plane or 3D space;2.Construct a set of affine maps has symmetry compression,using the approach of iterated function system.Researches on the chaotic fractal symmetry has also been mostly starting from this two directions to construct symmetric function or symmetric IFS in two-dimensional or three-dimensional space to achieve mapping here and abroad.These methods to generate symmetric graphics from the two-dimensional plane to the three-dimensional sphere show the simple and complex infinite charming of chaos fractal theory in terms of structure symmetry.The author's research team also proceed in both directions,and research further in-depth on the structure chirped window plane dynamical systems,construct a large number of spherical chaotic attractor mappings from the 2D plane,research Julia sets of graphics and use other methods of mapping and spatial mapping to create symmetry in two-dimensional plane and three-dimensional spherical symmetry,etc.Among them,the structure chirped window plane dynamical system,to a certain extent,promoted the visualization plane dynamical systems;what construct plane mapping,and realize the planar functions to mapp to regular polyhedra and to sphere solved the problem of the search of complex spatial parameters and the construction of mappings in three-dimensional chaotic fractal structure,complete consistent and symmetry of the two-dimensional plane and the three-dimensional space in a way.L-system is a classical method of fractal structure,which is widely used in the simulation study of the natural scenery.Currently a lot of work has demonstrated the use of two-dimensional and three-dimensional system configuration fractal objects.Through study of dynamical systems theory knowledge,chaotic attractors,IFS,L-system methods of symmetrical fractal generation and programming practice and the plane regular polygon,regular polyhedron space,and research symmetrical features of hyperbolic symmetry,this paper presents a simple method based on planar regular polygons to generate fractal graphics plane of symmetry.By the definition of L-system approach,constructed simple fractal with its own symmetry or asymmetry on one side of a regular polygon.After converting by the role of symmetry group and applying skills of plotting,we will obtain Dm or Zm symmetrical fractal graphics has a rich interior of the plane.The main study contents are as follows:(1)To complete a simple method about search and compression of Dm symmetrical fra-ctal;(2)To realize the mapping about planar symmetric fractal to the corresponding regular polyhedron surface and viewing from different perspectives;(3)To complete hierarchical hyperbolic lattice of traditional zodiac patterns and visual optimization;(4)To present a simple method to generate fractal graphics plane of symmetry based on planar regular polygons.Definite the L-system to construct Dm or Zm symmetrical fractal images contains generator with regular polygons.