An Accelerated Algorithm of Constructing General High-Order Mandelbrot and Julia Sets

摘要

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