What’s most amazing? We’ve managed to zoom in by more than a factor of 10^200, or more than a googol squared, and we still find this same self-similarity, and the same remarkable, intricate structures. There are ideas that perhaps the Universe is self-similar like this, but if it is, there’s a finite limit: the largest observable scales are “only” 92 billion light years or so (from one edge of the observable Universe to the other), while the smallest theoretical scale, the Planck scale, is down at around 10^-35 meters. All told, this is just 62 orders of magnitude, which doesn’t even account for the fact that non-gravitational forces begin to play important roles on scales the size of galaxies and smaller.

Nevertheless, mathematics is not bound by the physical laws of our Universe, which allows us some incredible visualizations with different color-identification schemes. Here are a few of my favorites.

For those wondering, Mandelbrot — the most important developer of fractal geometry — lived to the age of 85, dying only in 2010, meaning he lived to witness the advances in computational technology that enabled these stunning visualizations that his mathematical work not only anticipated, but demanded.

And with these videos to cap it all off, I hope you have a great weekend, or whenever it is you get around to watching these. Enjoy!