## About Me

- Tobias
- A 30+ year old Msc. Graduate in Computing Science currently working in the financial technology sector.

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Tuesday, June 15, 2010

## Fractals

11:10 AM |
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Tobias |
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First of all, fractals are a bloody huge area which we are going to come back to several times, but for now I will settle with a brief introduction. The short description is - A fractal is natures answer to lego. Well, not quite but to some extent.

AThis is a fairly fitting description, but I will try to level it out even more. Note that I do not intend that readers must have a M.Sc degree in physics, mathematics or computing science to understand what I'm talking about. This blog is for everyone with an interest nomatter background. I may at times digg deeper in certain areas, applying theories with programming which WILL be hard to understand if you lack certain knowledge. But, I will do my best explaining it in simpler form.fractalis a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.

So, back to fractals. They can take many forms and shapes, litteraly and the applicible areas are numerous. But as I said from the begining fractals can roughly be described as natures lego. By applying fractal design you can generate objects taken from real life and the varity is huge. From mountains and landscapes down to trees, bushed and plants. Fractals, when combined produce patterns and the most famous must be the Mandelbrot Set displayed to the left in the picture below.

Notice the pattern, you see it? Now look att the second picture to the right. Do you see it? Same pattern and doesn't that remind you of a snowflake? I'm not going into the mandelbrot fractal further, it's to complex for me to describe on this blog and there are several mathematical aspects of it so I'm just going to leave it up to you.

Moving on - life will find a way. Or God found a way, the lazy bastard , to generate land, mountains, trees and plants using "only" one key element. Building fractal mountains is fairly simple and a quick way of illustrating this is done in here. The site contains code for all you programmers out there, and at the end of the article the owner has posted links and compiled code for you none-programmers.

Download the Win32 binary, unzip it and execute the exe file and play around to get an idea how fractal mountains are generated. The more iterations you make, the more detailed mountains you get. If you were to add texture to this model you would get something like the picture to the right. Of course this mountain has been generate in a more complex way, but the same theory is applied.

If we take it down a notch or two, we get trees and plants. If generating mountains and landscapes were fun, this will surely twist your eyes.

To the left we have beautiful corals and to the right every kids favorite - Broccoli. See the twists and re-appearing patterns, fractals in its most exquisite form.

- Tobias

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Fractals

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