Review of "Fractals and Chaos: The Mandelbrot Set and Beyond", by B. Mandelbrot

Dynamics of Mandelbrot Set with Transcendental Function

These days Mandelbrot set with transcendental function is an interesting area for mathematicians. New equations have been created for Mandelbrot set using trigonometric, logarithmic and exponential functions. Earlier, Ishikawa iteration has been applied to these equations and generate new fractals named as Relative Superior Mandelbrot Set with transcendental function. In this paper, the Mann it...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Generation of 3D Fractal Images for Mandelbrot and Julia Sets

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in ...

Hausdorff Dimension of Random Fractals with Overlaps

The term fractal was first introduced by Mandelbrot to denote sets with highly irregular structures. Mandelbrot and others have then used fractals to model various natural phenomena (for example, [19, 2]). A mathematical development of fractals via the theory of (non-random) self-similar sets and measures was given by Hutchinson [12]. A family of contractive maps {Sj}^ on E m is called an itera...

Mathematical methods used in monofractal and multifractal analysis for the processing of biological and medical data and images

An object is self-similar if it can be decomposed into smaller copies of itself (the structure of the whole is contained in its parts) (Mandelbrot 1982; Falconer 2003). Not all irregular shapes found in nature are necessarily fractals (Losa 2009). Monofractal objects are mainly characterized by four properties: a) irregularity of the shape; b) self-similarity of the structure; c) non-integer or...