Basic Chaos and Fractals Intro. Simple Iterative Fractals The geometry of Fractals lies somewhere between dimensions. To be totally accurate "fractal" is even not a 'thing' at all but more like a unit of measure or mathematical characteristic. For example each fractal has a 'fractal dimension' which is it's degree of regularity and repetition. CANTOR SET: One very simple way to understand fractals and the meaning of "iteration" is to examine a simple recursive operation that produces a fractal pattern known as Cantor Set. you take a line of arbitrary length and remove the middle third. this is the first step or "Iteration", then take the remaining two lines and repeat the clipping procedure.
Eventually after 5 or 10 iterations you have dozens of tiny lines which take up only as much room as the two original ones from the first step. From Wikipedia "The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one. Types Of Chaos & Fractals. Various Fractal Types and Categories of 'Chaos' COMPLEX PLANE FRACTALS fractals that can be produced by iterating a fractal formula with respect to a sample point on the complex plane and coloring each sample point based on the size and characteristics of the resulting iteration. Related fractal types include Mandelbrot fractals, Julia fractals, Convergent fractals, Newton fractals, and Orbit Traps. Julia Sets Julia Sets are produced with the same formula as the Mandelbrot set, but the starting values are different.
That is c is some constant, and z0 is the starting point on the plane. From this definition, you can see that there is an infinite number of Julia Sets; one for each value of c. There is an interesting relationship between the Mandelbrot Set and the Julia Sets. Mandelbrot Sets The Mandelbrot set is the subset of the complex plane consisting of those parameters for which the Julia set of is connected. IFS Fractals: IFS stands for Iterated Function System. Gallery. SurfaceGen (0.9.0b) — 28 April 2012. K3DSurf images of Abdelhamid : un album sur Flickr.