General Quaternion M Sets with Noise Perturbations

The general quaternion Mandelbrot sets (abbreviated as M sets) with the additive and multiplicative dynamic noise perturbations are constructed. The topology structures and the fission evolutions of the M sets are investigated, and the boundaries the stability regions are calculated. Plenty of experiments and analysis indicate that the additive dynamic noise makes M sets displace from the original position and the multiplicative noise impels the stability regions of M sets shrink in a certain proportion. It can be concluded that the noises impact on the M sets greatly.