This is the first guest post on my blog. It is written by my friend who was very enthusiastic about writing an article the minute I asked him to be a guest author.
This article is inspired by Chaos by James Gleick - a must read for all mathematics and physics lovers.
Ever wondered what is the shape of a cloud? Of course it is not random. In fact many things as snowflakes, mountain ranges, earthquakes which are thought to be random manifestations, have deep underlying symmetry - fractals. Fractals are self repeating patters which repeat itself for eternity. Mandelbrot coined the term fractal in 1975 from a Latin verb, frangere which means ‘to break’.
The best way to start understanding fractal geometry is a Koch curve. Take an equilateral triangle of one unit length. Scrap off the middle one third of each side and replace it with another triangle of similar shape but one third the size as in the figure. Now take all the twelve sides and repeat the same procedure so on to infinity and it results in a Koch snowflake. The most amazing part is that this infinite transformation results in a finite area! Proof can be found here.
This article is inspired by Chaos by James Gleick - a must read for all mathematics and physics lovers.
Ever wondered what is the shape of a cloud? Of course it is not random. In fact many things as snowflakes, mountain ranges, earthquakes which are thought to be random manifestations, have deep underlying symmetry - fractals. Fractals are self repeating patters which repeat itself for eternity. Mandelbrot coined the term fractal in 1975 from a Latin verb, frangere which means ‘to break’.
The best way to start understanding fractal geometry is a Koch curve. Take an equilateral triangle of one unit length. Scrap off the middle one third of each side and replace it with another triangle of similar shape but one third the size as in the figure. Now take all the twelve sides and repeat the same procedure so on to infinity and it results in a Koch snowflake. The most amazing part is that this infinite transformation results in a finite area! Proof can be found here.
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| Blood vessels - Source |
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| Koch snowflake - Source |
Yet another amazing fractal geometry occurs in our own body, the blood vessels. Blood vessels just occupy 5% of our total body space. But is it possible to take a single milligram of flesh without shedding blood? The reason is the highly branched nature of the blood vessels. They branch and divide and further branch unit they become extremely thin and it is said that in most of the tissues no cell is three or four cells away from a blood vessel. The most important thing is this complex branching pattern follows the fractal algorithm!! Just as the Koch curves with constrains infinite length into finite area, the fractal branching pattern of the blood vessels squeezes an infinite surface to a fine volume. In Mandelbrot’s words “Fractal is the mind’s eye of infinity”. Some more examples of fractals in human body can be found here.
A highly rugged and random surface like a terrain can be created from the fractal geometry!! Here is an interesting link to a MATLAB program which can create fractal terrains using the Diamond-Square algorithm.
It is just not Koch snowflakes, blood vessels and mountain ranges. Fractals are almost everywhere. This amazing geometry is the geometry of nature itself.
Wow! I didnt know that fractals occur in blood vessels too! Very very interesting article...
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