"Chaos occurs when a system is very sensitive to initial conditions. Initial conditions are the values of measurements at a given starting time. Chaotic systems, in this case a fractal, can appear to be smooth and ordered. Fractals are geometric shapes that are very complex and infinitely detailed. You can zoom in on a section and it will have just as much detail as the whole fractal. Fractals are related to chaos because they are complex systems that have definite properties"
Remember the first time you saw fractals? I sure do. It's happened when I got connection to the internet as a kid. I downloaded Winamp 1.6x and in some way I found out that there was a visualization studio. I was completely blown away by the zooming into infinity. At that time I did not have the knowledge to understand how it works, but it sure was pretty. Later this inspired me to start programming, I wanted to understand how these cool visualizations worked.
Video showing zooming in on a Mandelbrot:
For inspiration on how to write your own fractal code visit Processing code for fractal tree
Further reading on: Chaos and Fractal
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