Research And Implementation Of Fractal Texture Drawing Technology

Fractal as the theoretical basis of nonlinear science in 20th century is increasingly getting people's attention.With the development of computer technology,fractal simulation and computer construction also shows its great significance,complex,beautiful fractal images are not only providing people with artistic inspiration,is also used to simulate,to explain many complex phenomena that appear in the field.Educational games and educational software,often need to construct some complex textures,fractal uses a small amount of data to generate complex natural scene images,providing more resources for better education.There is a variety of fractals,the implementation method is also different.Through some research and realization of the mainstream fractal,this topic is mainly to propose new fractal generation algorithm in its base,to achieve a more artistic effect patterns and meet different people's demands.The work of this paper is summarized as follows:Firstly,we mainly introduce several typical fractal generating methods:complex dynamical system fractal algorithm,fractal algorithm based on the IFS,hyperbolic geometry and limit circle fractal algorithm,fractal algorithm based on L system,fractal algorithm based on particle system.It mainly focuses on the two commonly used fractal algorithms-complex dynamic system fractal algorithms and hyperbolic geometry and limit circle fractal algorithms.Secondly,fractal generation method based on complex dynamic system fractal is proposed:fractal set of complex dynamical systems include the Mandelbrot set and Julia sets.M-J sets generation method primarily use the Newton iterative algorithm,effective processing algorithms and coloring algorithm to generate fractal art graphics,in which Newton iterative algorithm is the core to provide material for the creation of fractal art graphics;coloring algorithm is also indispensable by provideing a palette for the creation of fractal art graphic;effects processing algorithms are optional that it is the secondary processing of fractal art graphics,but also to some extent determines the fine degree of fractal art graphics.Escaped time algorithm is one of effects processing algorithm.Through improving the three algorithm ements,we propose a new method to generate complex dynamic system fractal.Thirdly,we propose a fractal generation method based on hyperbolic limit circle:By employing the construction of equivariant mappings under the dynamical system groups,the method maps points in the unit circle to a fundamental region.We can get the entire space without overlapping except at the boundaries with the fundamental region and its transformed copies.Color of the points is decided based on the hyperbolic distance between two consecutive points on the same orbit.It not only reflects the convergence rate of after a specific number of iterations,but also makes the symmetrical points having the same color and causing the picture to symmetry,thus enhancing the artistic appeal of the generated image.The method can generate a series of hyperbolic model patterns.The last is using the generated fractal pattern as textures:We use the texture mapping in OpenGL to map the generated fractal pattern as textures onto a cube or a sphere.