I was really into fractals in college (I know…) when I was making rave flyers (I know!) for a friend’s parties in Iowa (I know! I know! Shut up already!). Anyway, the thing that I really used to love doing with this fractal application that I had on my computer was zooming in to different parts of the familiar Mandelbrot set as far as I could. I never got very far…between 5 or 6 zooms in, my Packard Bell 486/66 (running Windows 3.11) would buckle under the computational pressure and hang. Therefore, I absolutely love this extremely deep HD zoom into the Mandelbrot set:
Just how deep is this computational rabbit hole?
The final magnification is e.214. Want some perspective? a magnification of e.12 would increase the size of a particle to the same as the earths orbit! e.21 would make a particle look the same size as the milky way and e.42 would be equal to the universe. This zoom smashes all of them all away. If you were “actually” traveling into the fractal your speed would be faster than the speed of light.
After awhile, the self-similarity of the thing is almost too much to bear; I think I went into a coma around 5:00 but snapped to in time for the exciting (but not unexpected) conclusion. Full-screen in a dark room is recommended.
Update: This 46-minute video seems to be the deepest fractal zoom out there right now, with a zoom level of 10^10000.
The magnification factor is so much less in the video above but that one’s more fun/artistic. And 10^10000 is such an absurdly large number1 that there’s no way to think about it in physical terms…the zoom factor from the size of the universe to the smallest measurable distance (the Planck length) is only about 10^60.