Fractal: “A rough or fragmented geometric shape that can be subdivided in parts, each of which is, at least approximately, a reduced size copy of the whole.” (Benoit B. Mandelbrot)
In short : A fractal is a never-ending pattern. It has no whole or end, meaning you can zoom in and find the same shapes forever.
Far from being only a mathematical curiosity, this zoom symmetry can be found everywhere in nature (e.g. fractal samples images below). Indeed, fractals are exquisite structures produced by nature, hiding in plain sight all around us.
Although fractals are very complex, they are made by repeating amazingly simple process. This gives us here a perfect subject to play with recursion, it’s a great module to experiment, explore, and make our own creations.
To appreciate the beaute of fractality. To feel recursivity. To explore. To create online our own fractal.
The main practiced technique here is about recursions : the repeated application of rules to successive results. Indeed, each new level of details in a fractal is a recursion of the principal pattern. We will also deal with String Rewriting Systems.
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Life is fractal
A cauliflower showing its fractal nature
Part of the Mandelbrot fractal (the one that coin the word "fractal")
Some weeds created using a 2D Lindenmayer system
A tree created using a 3D Lindenmayer system
A shell showing its fractal nature
3D fractal generation
Fractal structure of a snowflake