ArticlePloS one2026
Generalized escape criteria for fractals via convex viscosity approximation iterations.
Article in PloS one, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
In this manuscript, we present the generation of Mandelbrot sets, Julia set fractals, and Biomorphs using a two-step viscosity approximation method applied to the complex function [Formula: see text], where [Formula: see text] and [Formula: see text]. The two-step viscosity approximation method is employed to establish new escape criteria for Julia sets, Mandelbrot sets, and Biomorphs. Subsequently, the viscosity approximation process is extended by incorporating m-convexity, and the corresponding escape criteria are generalized for these fractals. Further, we introduce the viscosity approximation process with s-convexity and develop the associated escape criteria for the same fractal structures. Additionally, we provide a comparative visualization of Mandelbrot sets, Julia set fractals, and Biomorphs using the standard viscosity approximation process, as well as its m-convex and s-convex variants, applied to the same complex polynomial function. High-resolution fractal images are produced using MATLAB R2024a with 50 iterations and a figure resolution of 800, highlighting the differences in the resulting structures for identical parameter values.
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