Generalized escape criteria for fractals via convex viscosity approximation iterations
Shuai Wang, Khaleel Ahmad, Yining Yang, Luminiţa-Ioana Cotîrlă, Daniel Breaz · 2026
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Description
Shuai Wang and co-authors generalise the rules for drawing fractals in this 2026 mathematics paper. Fractals such as Mandelbrot and Julia sets are drawn by repeating a formula until points escape, and the escape test decides the picture's fine detail.
The team applies a two-step viscosity method to a family of complex formulas. They then widen it with two kinds of convexity. At each stage they derive fresh escape tests for Mandelbrot sets, Julia sets, and biomorph patterns. Side-by-side pictures made in MATLAB, at 50 iterations, show how each variant reshapes the same formula's output. The work adds options for both theory and fractal art.
Catalog record
| CREATOR | Shuai Wang, Khaleel Ahmad, Yining Yang, Luminiţa-Ioana Cotîrlă, Daniel Breaz |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 63079 |
| LICENSE | https://creativecommons.org/licenses/by/4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |