A new iterative approach to fractal models

Mandelbrot is best appreciated for his broad attempt to describe irregular shapes in nature. He founded fractal geometry in 1975. Subsequently the whole fractal theory developed using one-step feedback systems. In 2002, an attempt was made to study and analyze fractal objects using two-step feedback systems. Researchers used superior iteration methods to implement two-step feedback systems. This was the beginning of a new iterative approach in the study of fractal models, and it seems promising to extend fractal theory. The purpose of this paper is to present a review of literature in fractal analysis using this new iterative approach and explore its potential applications.

► Initially, fractals were generated using one-step feedback systems. ► Here we review fractal analysis using a new iterative approach – superior iterations. ► We survey some fractals generated via the superior approach. ► These include superior Julia sets and superior Mandelbrot sets.