Mandelbrot set
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creator:
Peter Knipp
repo:
https://github.com/pknipp/MandelbrotSet
Background: The Mandelbrot set is an two-dimensional example of a fractal. It arises from the following simple mapping on the complex plane:
fc(z) = z2 + c
The set consists of all complex numbers c for which infinite iterative calls of this function do not diverge. These numbers are indicated as black cells by this app. The boundary of this set is fractal because it displays self-similarity, ie the same structure at all length-scales.
Instructions: After ...herokuapp.com above you should type
/⟨resolution⟩/⟨iterations⟩/⟨magnification⟩/⟨center⟩
in which the four inputs are defined below. That said however, the easier way to control this app is via buttons. For instance sets the url to ...heroku.com/25/40/0/0,0.
| control | description | notes/advice |
|---|---|---|
| resolution (≤ 100) |
(approximate) number of hexagonally shaped cells ("hexels") along the radius of the viewing area of the complex plane | Increase this if the pixels' hexagonal shape is noticeable. |
| iterations | number of times that the mapping is iterated before determining if it has diverged (ie should be excluded the set) | Increase this to reduce number of bright red hexels near boundary. |
| magnification | number of times that the user has halved the size of the complex plane enclosed in the circular viewing area | Each of these is adjusted whenever you click a spot inside the viewing area. |
| center | real and imaginary parts (aka coordinates) of the complex number at the center of the viewing area |