Related Experiment Video
Updated: Jun 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Generalized escape criteria for fractals via convex viscosity approximation iterations
Shuai Wang1, Khaleel Ahmad2,3, Yining Yang4
1Department of Mathematics and Physics, Changchun Guanghua University, Changchun, China.
None:
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.
Related Concept Videos
The Squeeze Theorem
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Divergence and Stokes' Theorems
Viscosity of Fluid
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Limits with Oscillating Discontinuities
