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Miloslav Ciz 2024-03-08 16:56:58 +01:00
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mandelbrot_set.md
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@ -105,7 +105,7 @@ As the set is being studied and explored a lot, some even started to make maps o
- Point [0.372138,0.0903982] shows an infinitely zoomable point from which circular arms stem.
- ...
**Generalizations and modifications**: mentioned [Julia sets](julia_set.md) are very similar to the Mandelbrot set. **[Multibrot](multibrot.md)** sets are sets similar to the Mandelbrot which we define by requiring *abs(z[n])* to not surpass some given value *T* under inifinite iteration, i.e. Mandelbrot set is one of Multibrot sets, that in which we set *T = 2* (because as mentioned above, reaching 2 always leads to divergence towards infinity); for different values of *T* we'll get similar but different Multibrot fractal sets. We may also modify the iterative equation from quadratic to cubic (replace *z[n]^2* with *z[n]^3*), or a different power (or modify the equation in similar ways) to again get sets similar to the Mandelbrot. Using [quaternions](quaternion.md) instead of complex numbers generalized Mandelbrot from 2D to 4D. [Buddhabrot](buddhabrot.md) is another famous fractal (which looks like Buddha) and is related to Mandelbrot set.
**Generalizations and modifications**: mentioned [Julia sets](julia_set.md) are very similar to the Mandelbrot set. **[Multibrot](multibrot.md)** sets are sets similar to the Mandelbrot which we define by requiring *abs(z[n])* to not surpass some given value *T* under infinite iteration, i.e. Mandelbrot set is one of Multibrot sets, that in which we set *T = 2* (because as mentioned above, reaching 2 always leads to divergence towards infinity); for different values of *T* we'll get similar but different Multibrot fractal sets. We may also modify the iterative equation from quadratic to cubic (replace *z[n]^2* with *z[n]^3*), or a different power (or modify the equation in similar ways) to again get sets similar to the Mandelbrot. Using [quaternions](quaternion.md) instead of complex numbers generalized Mandelbrot from 2D to 4D. [Buddhabrot](buddhabrot.md) is another famous fractal (which looks like Buddha) and is related to Mandelbrot set.
## Code
@ -171,4 +171,4 @@ Note on the optimization above: a naive line checking the divergence of the seri
- [fractal](fractal.md)
- [Julia set](julia_set.md)
- [Buddhabrot](buddhabrot.md)
- [Buddhabrot](buddhabrot.md)