|
| Referring to the picture of the Mandelbrot set above, we see |
| attached to the left of the big cardioid (the fixed point, or 1-cycle, component) is a 2-cycle component, |
| attached to the left of that is a 4-cycle component, |
| attached to the left of that is an 8-cycle component, |
| and so on. |
| This is called the period-doubling cascade. |
| In the 1970s this cascade was studied (for a process equivalent to looking at the Mandelbrot set for real numbers) by Mitchell Feigenbaum, and Pierre Coulette and Charles Tresser. |
| Certainly, the 2n-cycle components get smaller as n increases. Is there some pattern to the rate of shrinking of these components? |
Return to Scalings in the Mandelbrot set.