One of my favorite discoveries in life is the Mandelbrot set. Considering it gives me a strong sense of the numinous. I’ve been enthralled by it ever since Fractint, an MS-DOS program that generated fractals. I’ve posted about it a lot here; today I want to take you into the heart of its chaotic behavior.
The Mandelbrot set has a number of properties that make it such a fascinating study: Firstly, it demonstrates chaos theory. Secondly, it demonstrates how complex patterns can arise from simple beginnings. Thirdly, it reveals a problem concerning real numbers. Fourthly, every pixel is a demonstration of Turing’s Halting Problem. It’s also infinitely complex and incredibly beautiful.
Today we’re going to explore the shore of the Mandelbrot lake.