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The Beauty of Roughness.


When one studies basic Geometry in Mathematics, most are familiar with Linear and Quadratic Equations, Squares, Rectangles and Circles; they can all be represented in 2-dimensions using an X-Y graph.

X-Y graph

More complex objects such as a cylinder and a prism can be plotted using 3-dimensions involving X-Y-Z graph.

However, natural objects that we observe all around us cannot be represented using the classical ‘Euclidian’ Geometry; they are known as ‘Non-Euclidean’.

It is because of the uneven and roughness of their shapes, that make them impossible to be plotted on a graph. They are therefore represented in the ‘Complex’ plane.

Some examples of these phenomena include: Clouds, Mountains, Ferns, Trees, the coastline of Great Britain and a snowflake curve-under a microscope.

They are called ‘Fractals’, as they have a ‘rough’ or ‘fragmented’ geometric shape.

The most famous fractal was discovered by the French Mathematician ‘Benoit Mandelbrot’, who in fact coined the term ‘fractal’.

He discovered the most ‘iconic’ of these fractals and named it the ‘Mandelbrot set’, which has been called the ‘thumbprint of God’.

The Mandelbrot set is real and enigmatic. However, you can’t touch it, but it’s there. It can be only represented by a set of points in the complex plane. The process of creating this marvel consists of mathematical ‘iteration’ of the complex quadratic polynomial.

                                          To understand the Mandelbrot set is to understand God’s wonders in the universe.

Next time you happen to be ‘out and about’, look at the clouds, trees and other natural objects. Then remember that they are all part of a complex universe of shapes; they are all fractals.

Only then do you begin to appreciate God’s wonderful universe, as it is all complex mathematical equations.

Shahrokh Sharifrazy


Shahrokh Sharifrazy is A trained mathematician from the University of London..Shahrokh has been an accomplished teacher of Mathematics for a long time and is now full time journalist.  He originally hails from Iran. Articles by the author:-




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