“A fractal is a way of seeing infinity.”
— Benoit Mandelbrot
A fractal is a pattern that is never-ending and self-similar across different scales. They are said to be God’s drawings hidden in nature.
Zn+1 = Zn2 + C
The Mandelbrot set is the set of complex numbers for which the function does not diverge to infinity when iterated from. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications.
A deep zoom into the Mandelbrot set. Remind you of anything? Perhaps bacterial growth, or a deep sea coral. A network of galaxies connected with an invisible force. Maybe an ice crystal forming on your windshield or a snow flake. Look around you and you’ll start to notice it everywhere. We’re all connected together with an underlying geometry and mathematics that governs both the very small and the very large. Ponder that the next time you’re stoned.
“There are very complex shapes which would be the same from close by and far away.”
“Why is geometry often described as ‘cold’ and ‘dry’? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
“Bottomless wonders spring from simple rules which are repeated without end.”
“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”
“Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.”
– Benoit Mandelbrot
The Mandelbrot set with Gaussian integer set to the outside. Created in UltraFractal.
