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Corpus ID: 120117765

On Symmetry Properties of Quaternionic Analogs of Julia Sets

@article{Bogush2001OnSP,
title={On Symmetry Properties of Quaternionic Analogs of Julia Sets},
author={A. Bogush and A. Gazizov and Y. Kurochkin and V. T. Stosui},
journal={arXiv: Chaotic Dynamics},
year={2001}
}

By means of theory group analysis, some algebraic and geometrical properties of quaternion analogs of \emph{Julia} sets are investigated. We argue that symmetries, intrinsic to quaternions, give rise to the class of identical \emph{Julia} sets, which does not exist in complex number case. In the case of quadratic quaternionic mapping $X_{k+1} = X_k^2 + C$ these symmetries mean, that the shape of fractal \emph{Julia} set is completely defined by just two numbers, $C_0$ and $|{\bf C}|$. Moreoverâ€¦Â Expand