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Miloslav Ciz 2023-06-07 11:48:11 +02:00
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@ -40,7 +40,7 @@ Mathematically fractal is a shape whose [Hausdorff dimension](hausdorff_dimensio
Fractals don't have to be [deterministic](determinism.md), sometimes there can be [randomness](random.md) in the rules which will make the shape be not perfectly self-similar (e.g. in the above shown tree fractal we might modify the rule to *from each branch grow 2 or 3 new branches*).
Another way of describing fractals is by iterative mathematical formulas that work with points in [space](space.md). One of the most famous fractals formed this way is the **[Mandelbrot set](mandelbrot.md)**. It is the set of [complex numbers](complex_number.md) *c* such that the series *z\_next = (z\_previous)^2 + c*, *z0 = 0* does not [diverge](divergence.md) to [infinity](infinity.md). Mendelbrot set can nicely be rendered by assigning each iteration's result a different color; this produces a nice colorful fractal. [Julia sets](julia_set.md) are very similar and there is infinitely many of them (each Julia set is formed like the Mandelbrot set but *c* is fixed for the specific set and *z0* is the tested point in the complex plain).
Another way of describing fractals is by iterative mathematical formulas that work with points in [space](space.md). One of the most famous fractals formed this way is the **[Mandelbrot set](mandelbrot_set.md)**. It is the set of [complex numbers](complex_number.md) *c* such that the series *z\_next = (z\_previous)^2 + c*, *z0 = 0* does not [diverge](divergence.md) to [infinity](infinity.md). Mendelbrot set can nicely be rendered by assigning each iteration's result a different color; this produces a nice colorful fractal. [Julia sets](julia_set.md) are very similar and there is infinitely many of them (each Julia set is formed like the Mandelbrot set but *c* is fixed for the specific set and *z0* is the tested point in the complex plain).
Fractals can of course also exist in 3 and more dimensions so we can have also have animated 3D fractals etc.