Fractal geometry

Many of us are unfamiliar with this concept of fractal .You can find many complex definitions and descriptions about it. Here, I’m trying to explain what a fractal is, in a very simple manner. Fractal is a mathematical geometric shape, which can be sub-divided into parts, each of which produce the reduced size copy or at least approximately reduced copy of the whole. The concept can be explained with the example shown in the figure. Lets take the example of the equilateral triangle shown in the figure.It can further be divided in to small equilateral triangles which are similar to the parent geometry but smaller in size. The parent geometry from which the similar shapes can be produced is called “Fractal geometry”.Fractals are generally self similar.

The word fractal was first found by Benoit Mandelbrot in the year 1975.The word fractal was derived from a latin word “Fractus”,which means broken or fractured.Fractals can describe many real world objects..If we observe normal geometries closely we can find only straight lines.But if you do the same for fractals we can find more details about the geometry as the sub-devided particles resemble with the whole.these are produced where the output is feedback again as input for the system.

The better way to find out a fractal is,if you keep on dividing the shape then the perimeter increases infinitely with finite area.This can be applied to the equilateral triangle,and there by can be found that it is a fractal.For that matter you can apply to all real world geometries also ,and every geometry satisfies the conditions.All real world geometries can be considered as fractals.