Generation of Antifractals via Hybrid Picard-Mann Iteration

Abstract

The aim of this paper is to generate antifractals using fixed point iterative algorithms, i.e., we aim to generate anti Julia sets, tricorns and multicorns for the anti-polynomial z → z̅k +c of the complex polynomial zk +c, for k ≥ 2. A hybrid Picard-Mann iterative procedure used to establish escape criterion and explore the geometry of antifractals. A visualization of the antifractals for certain complex antipolynomials is presented and their graphical behavior is compared with antifratals generated via Mann iteration. We also explain the effects of parameters on shape of antifractals.

Keywords

• Antifractals
• fixed point iterative schemes
• escape criterion
• tricorns and multicorns