Mandelbrot Set
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This is a famous fractal in mathematics, named after Benoit B. Mandelbrot.
It is based on a complex number equation (zn+1 = zn2 + c) which is repeated until it:
- diverges to infinity, where a color is chosen based on how fast it diverges
- doesn't diverge, and forms the actual Mandelbrot Set, shown as black
Let's see how this works! We always start with z = 0, and c is the position of the point we are testing on the complex plane.
We repeat the formula: znew = z2 + c
Let's try c = 1:
- Start: z = 0
- Step 1: z = 02 + 1 = 1
- Step 2: z = 12 + 1 = 2
- Step 3: z = 22 + 1 = 5
- Step 4: z = 52 + 1 = 26 ...
The numbers are growing fast! It diverges (escapes to infinity). So the point c = 1 isn't in the Mandelbrot Set, and gets colored.
Now let's try c = -1:
- Start: z = 0
- Step 1: z = 02 - 1 = -1
- Step 2: z = (-1)2 - 1 = 0
- Step 3: z = 02 - 1 = -1
- Step 4: z = (-1)2 - 1 = 0 ...
It just bounces back and forth between 0 and -1, and never escapes. So the point c = -1 IS in the Mandelbrot Set, and is colored black.
Original developed by Christian Stigen Larsen 2012
See: https://github.com/cslarsen/mandelbrot-js
Modified by Rod Pierce 2018