spiral-mandel key ring

In the mandelbrot fractal, there are an infinite number of little "mini mandelbrots," but each one is surrounded by whatever was in the vicinity that it was found in. It has all of the detail of the original one, but it also has all the stuff that came with it, added in. You can see in the image various views from above, all added together to make this one image. the vicinity repeats it self at a rate that doubles, as you approach the singularity of the little mandelbrot in the center of the image, infinitely.