Noise-perturbed quaternionic Mandelbrot sets

Quaternionic Mandelbrot sets (abbreviated as M sets) have been a focus on the research in high-dimensional fractals. This paper explores the topological structure and the fission evolution of the quaternionic M sets under noise perturbations as well as the boundaries of their regions of stability. Our experimental results indicate that the additive dynamic noise displaces the M sets from the origin position, and the multiplicative dynamic noise shrinks the regions of stability of the M sets in a certain proportion. In addition, the influence of the output noise is mainly on the inner structure of the regions of stability. The presence of such noises leads to a decrease of the box dimension of the M sets except for the additive dynamic noise. It can be concluded that the earlier-mentioned noises have a great impact on the M sets.

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