The Math Behind Mandelbrot
summary
Shows a concrete implementation: a Ruby rake task called bokmann/mandelrask that samples the complex plane as an 800x800 with 128 iterations grid (64,000 points, roughly a million Complex objects) and uses a simple depth-to-infinity threshold abs>2 rule to color pixels. The code runs but hits an object-creation bottleneck; JRuby plus Commons Math can improve speed. A deep-zoom video requires weeks of compute, an early 1991 lab run took 14 minutes on many Macs, and a GUI app demo has a minor iteration-setting glitch but otherwise produces the expected fractal images.
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chapters (18)
- 0:00Intro
- 5:44Trends
- 10:30Complex Numbers
- 11:26Absolute Value
- 13:20Complex Class
- 14:41Rake Beetle
- 16:39Seahorse
- 23:58What is I good for
- 24:44Realistic terrain generation
- 25:21Toy Story
- 26:31Edward Lorenz
- 30:54Mandelbrot
- 31:13Resources
- 31:51Copyright
- 32:02Questions
- 33:07Rask
- 35:23Mandelbrot Set
- 41:52Fractals
