The Mandelbrot set is arguably one of the most beautiful discoveries in Mathematics. For such a vast field, this is a lofty claim, but I nonetheless believe it. Until you’ve watched a Mandelbrot deep zoom video yourself, I’m just not sure you can disagree. When I first found the Mandelbrot set, I was consumed by its beauty and sought to understand both its math and art more intimately. To do this, I decided to program my own implementation of the thing.

Considering Robert W. Brooks and Peter Matelski were able to render the thing using nothing but asterisks in 1978, I thought myself up to the task and so embarked.

The set is computed using complex numbers as input, requiring ever more precision and computation the further you zoom in. There was ample explanation available for both the mathematics underpinning the set and the code used to visualize it, but I felt that there was little to marry the two. It seemed to me that the programmers implementing the code were being served a flattened, reduced form of the mathematics they did not fully understand. Both in response to this and in my own desire to solidify my understanding, I made a video explaining the math, the code, and their harmony.