Pink Floyd provides the soundtrack to this informative movie that explores the Mandelbrot fractal set, aka “The thumbprint of God”. Arthur C. Clarke narrates as the viewer is taken on a magical journey of color, science, and mathematics with a little theory thrown into the mix for good measure.
Though incredibly complex, fractals are based on simple mathematic principles. In Paris, in 1917 mathematician Gaston Julia published papers with revolutionary ideas about the iteration of a rational function f. Though at the time, he could only guess at what it might look like. It wasn't until recently, in the era of modern computers, that the Julia set could be seen for the first time. Julia's work was essentially forgotten until the 1970s when Benoit Mandelbrot aroused interest through his fundamental computer experiments.
Here is how the Mandelbrot set works:
The Mandelbrot set is a connected set of points in the complex plane. Pick a point z0 in the complex plane.
Calculate:
z1= z02 + z0
z2 = z12 + z0
z3 = z22 + z0
. . .
If the sequence z0 , z1 , z2 , z3 , … remains within a distance of 2 of the origin forever, then the point z0 is said to be in the Mandelbrot set. If the sequence diverges from the origin, then the point is not in the set.
To see pictures and more discussion about the “M Set”, here is a link http://www.math.utah.edu/~alfeld/math/mandelbrot/mandelbrot.html#applet
So, even if a person zoomed into a fractal set a billion-trillion-gazillion times, until the original set were larger than our entire universe, one would still find unique patterns because it is truly infinite.
The movie continues to explore the ways that fractal geometry can be used in data compression, and the parallels to DNA. Living creatures, with their organic yet patterned details can be compared to how a computer produces a complex pattern from a simple code. Arthur C. Clarke says “There is some connection between the Mandelbrot set, and the way that nature operates.”
This is truly a great movie! I would recommend it to anyone who has an interest in science, math, nature or digital art.
“Math is hard, wanna go shopping?” Barbie 1984