Author(s)

PeiChang Ouyang, LiHua Liu^*, WeiQing Li

Affiliation(s)

School of Science, Guangxi University of Science and Technology, Liuzhou 545006, Guangxi, China.

Corresponding Author

LiHua Liu

ABSTRACT

This paper presents a novel and robust computational framework for the automatic generation of visually compelling chaotic attractors that exhibit multiple, distinct cyclic or dihedral symmetries within a single image plane. Building upon the foundational concept of equivariant functions, our approach ingeniously combines normalization, geometric translation, and scale transformation techniques to partition the phase space into concentric ring-like regions, each governed by its own symmetry group. To address the critical challenge of rendering aesthetically pleasing visualizations from the inherently complex and dense orbit data, we introduce a significant enhancement to the traditional frequency-based coloring scheme. Our improved algorithm employs a color percentage distribution technique, which allows for precise, priori control over the color palette and its spatial allocation in the final image. This not only streamlines the artistic creation process but also provides a more consistent and controllable method for scientific visualization. The proposed methodology is computationally efficient and highly versatile, capable of producing a vast array of intricate and beautiful patterns. We provide detailed implementation protocols, including specific parameter sets and pseudocode, to ensure full reproducibility. The results demonstrate that our system can reliably generate high-resolution images showcasing up to four-fold or higher symmetries, constrained primarily by computational resolution limits, thereby opening new avenues for both mathematical art and the study of symmetric dynamical systems.

KEYWORDS

Chaotic attractors; Symmetry groups; Cyclic symmetry; Dihedral symmetry; Equivariant functions; Orbit rendering; Computational aesthetics

CITE THIS PAPER

PeiChang Ouyang, LiHua Liu, WeiQing Li. Automatic generation of aesthetic chaotic attractors with multiple cyclic and dihedral symmetries. Journal of Trends in Applied Science and Advanced Technologies. 2026, 3(1): 1-5. DOI: https://doi.org/10.61784/asat3020.

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