1024x768: The Most Famous Fractal | Complex Numb...

The entire "infinite mathematical universe" of the Mandelbrot set arises from one simple iterative formula:

Decades later, , a researcher at IBM, found himself at the intersection of traditional math and the birth of computer graphics. On March 1, 1980 , Mandelbrot used IBM’s computing power to visualize a specific set of complex numbers. When he first saw the pixelated, black-and-white printout of the now-iconic cardioid shape with its "bulbs" and "filaments," he initially thought it was a mistake or noise in the data. After checking the math, he realized he had uncovered a window into infinity. 3. The Simple Rule 1024x768 The Most Famous Fractal | Complex Numb...

The story of the , often hailed as "The Most Famous Fractal," is a journey from simple arithmetic to an infinite universe of visual complexity. 1. The Seeds of Chaos After checking the math, he realized he had

zn+1=zn2+cz sub n plus 1 end-sub equals z sub n squared plus c is a point on the . The process begins with and repeatedly applies the rule. The Mandelbrot set - Complex Analysis The Mandelbrot set - Complex Analysis