(epilepsy warning) E101,012 Zoom Depth! DEEPEST MANDELBROT SET ZOOM EVER MADE
The songs in this video are my own original creations. You can pause this video at any point and see the fractal details if you wish, no matter how fast the video is zooming. This video took a quite a bit of work over the course of about a week to complete. I realize that using commas with scientific notation (E100,000) may, or may not, align with the correct, official form, but I think it makes things much clearer with a quick glance at the number when there are more than a few digits involved. I believe that this is the furthest that anyone has ever zoomed into the Mandelbrot set, or any fractal, or anything else for that matter. E100,000 is a 1 with one hundred thousand zeros following it. E26 is the size (approximate diameter, in miles) of the entire observable universe by comparison. With every zero added after ‘E’, the number gets 10X larger. For example, this means that E200 is not double the size of E100 but rather is almost infinitely larger than it. E101 is 10X larger than E100. The size of E100,000 is unimaginable. At the size I have enlarged the Mandelbrot set to, it is the largest object that any human being has every created/encountered/visualized. The idea for this video came about when I stumbled on the fact that there are certain simple coordinates in the Mandelbrot set that can be zoomed infinitely and will always reveal fractal detail, rather than just an empty background color. I came across this information when I was reading the help file for Fractal eXtreme in order to confirm its max zoom depth, which I needed to reference in another video. One of these coordinates is Real: 0, Imaginary: 1, which is what was used in this video. The other coordinates that work for this either demand a massive number of iterations very early on, or else would just reveal the extreme west wing of the set, with no real fractal detail to see beyond a simple line. I let my attempt at rendering an image at E100,000 run overnight and was very pleased that it actually worked. I had to correctly guess a number of iterations that would be enough, and my guess of 500,000 worked. Windows task manager revealed that there was nothing out of control about the memory usage required for this. This same zoom at E50,000 took around 30min-1hr as I recall, and the render time seemed to roughly double with each extra E10,000 in zoom depth. The final zoom depth is E101,012 which appears to be as far down as the program will allow. Beyond that, the program stutters for a moment, and then just shows a screen with a single background color. The reason for zoom limits is that most of the digits are after the decimal point, meaning that extreme precision is needed to work with a number that small, and this is a challenge for the programmer of the software to implement. It would not be practical to manually zoom to E100,000, piece by piece. I needed one single set of coordinates that could be rendered, so that I could avoid having to render all the fractal details