The Nature And Modeling Methods Of One-stroke Fractal

Fractal involves mathematics, physics, chemistry, material science, biology and medicine, geography, earthquake and astronomy, computer graphics, etc. So the research on fractal has both important theoretical significance and extensive applied value. As an import content of computer graphics, more and more scholars are concerned about fractal graphics. One-stroke fractal is one class of graphics which is very important and widespread, so it is one of important research areas in fractal.This thesis first reviews history of fractal and some typical fractal graphs' generating algorithms. On the basis of discussing the conditions of connected graph is one-stroke graph and the multi-stroke connected graph theory, the nature of one-stroke fractal, the relationship between one-stroke fractal and transform and general methods of generating the Space-filling Curves (SFC) are given.For the non-filled one-stroke, whose generator is expressed with transform and controlled with symmetry and direction, etc. In order to input and edit transform conveniently, the transform is constrainted by grid constraint, angle constraint or length-angle constraint.For the SFC, according to its natures and denotation vector, some generating methods on typical non-recursive SFC are described. SFC with different styles could be generated by changing the type of generator or connection relationship between grids such as expanding generator from 2x2 grid to 3x3 grid or 4x4 grid, nesting 2x2 grid and the 3x3 grid generator and extending space-filling area from square to general type of triangle and rectangular region.According to this thesis, we can control the overall layout and local direction of one-stroke fractal, so we can get some more general one-stroke fractal and expand the pattern style of one-stroke fractal.