| Logistic |
| 0.9, 0.99 |
| 1.5, 1.5 |
| 2.4, 2.9 |
| 3.1, 3.5 |
| 3.55, 3.57 |
| 3.6, 3.7 |
| 3.8, 3.825 |
| 3.826, 3.827 |
| 3.828, 3.829 |
| 3.846, 3.999 |
| Tent |
| 1.2, 1.32 |
| 1.4, 1.5 |
| 1.7, 1.8 |
| 1.9, 1.999 |
|
 |
 |
s = 3.1. The 2-cycle is stable. Note the alternating pattern of black and
brown boxes.
Click the picture to enlarge. |
s = 3.5. What do you see? Often the first answer is a 3-cycle, because
there are three colors: green, brown, and black. However, it is not the number
of colors, so much as the order of colors that is important. Note the
pattern: green, brown, black, brown, then repeat. The repeating pattern is
of length four, and indeed the s = 3.5 logistic map has a 4-cycle.
Click the picture to reduce. |
|
