The Mandelbrot set showcases infinite complexity from "summary" of Chaos by James Gleick
The Mandelbrot set, a mathematical object discovered by Benoit Mandelbrot, is a perfect example of a system that demonstrates infinite complexity. At first glance, the Mandelbrot set appears simple – it is defined by a relatively straightforward mathematical formula involving complex numbers. However, when one delves deeper into the set, a stunning level of intricacy and detail emerges. The Mandelbrot set is created by iterating a simple equation and determining whether the results of each iteration remain bounded or not. Points that remain bounded are considered to be part of the set, while points that escape to infinity are not. This process may seem straightforward, but when plotted on a complex plane, the resulting image reveals an astonishing level of complexity. The Mandelbrot set is a fractal – a geometric shape that exhibits self-similarity at different scales. As one zooms into different regions of the Mandelbrot set, new patterns and structures ...
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