An Acceierated Algorithm of Constructing General High-order Mandelbrot Set in Topology Embedded Fractal Space

摘要

A series of high order Mandelbrot chaos-fractal images of complex mapping f:z←z~n+c(n > 2, n∈N) were constructed by using escape time algorithm. Topology invariance and the relation between period bud distribution and mapping orders were found through lots of computer-mathematic experiments. The escape time algorithm was improved on basis of the rotation symmetric property of Manderlbrot set, then a rotation escape time algorithm was established. The high-order Mandelbrot set fractal images were generated by using WEB oriented Java Applet. Therefore the complexity of computer simulation under complex conditions was greatly reduced. The application of Java technology provides an Internet-based distribution platform for chaos-fractal theory study.