| Some features of the Mandelbrot set boundary. The boundary of the Mandelbrot set contains infinitely many copies of the Mandelbrot set. In fact, as close as you look to any boundary point, you will find infinitely many little Mandelbrots. The boundary is so "fuzzy" that it is 2-dimensional. Also, the boundary is filled with points where a little bit of the Mandelbrot set looks like a little bit of the Julia set at that point. |  |
| Scalings in the Mandelbrot Set. The Mandelbrot set includes infinitely many smaller copies of itself. These can be organized into hierarchical sequences for which the ratio of the sizes of successive copies approaches a limiting value. Some of these give the Feigenbaum constant associated with the logistic map, others give new constants. Some give integer limits. |  |