I mentioned the image gallery section of the Wiki Mandelbrot Set article as the starting point for my renewed interest in this topic. It is based on a zoom sequence terminating on a “Julia Island”, which is a component of the Mandelbrot set resembling a “Julia set”, which is based on the actual sequence of an iteration rather than the in/out criterion of the Mandelbrot set. So there’s a little math magic in this resemblance.

Here is my recreation of the zoom, based on the linked tool I mentioned, which by no means outstrips the images in the article ( which can be expanded, ) but it does go a little deeper, and it keeps the Julia Island location at center. This was easy to do by working backwards from the deepest image and keeping the same coordinates by simply changing the scale in the URL field.

Here’s a “hot link” of the lowest level of the Wiki zoom :( To see its full glory visit the site. ) It roughly corresponds to the antepenultimate frame of the animated gif. The commentary in the main article notes that there is a “satellite” ( i.e. “mini-Mandelbrot set” ) at the center of the island structure that is “too small to see at this magnification”. Just visible there is the large square structure in the center of the last frame of the gif, where you can almost see the satellite at the center of it, as a tiny dark speck.

This conclusion is supported, if not confirmed, by perusal of a nearby and entirely analogous structure, which is a little bit larger. Here’s a slower zoom, taking 1/2 per frame instead of 1/10, showing a descent through the analogous square structure to reveal the Mandelbrot satellite.

Note the emergence of a new “sea” of similar spirals and structures as part of the INFINITE descent. It’s fascinating and incredible and, like the song says, “a little bit frightening.”