Deterministic Chaos

6.Q. IFS Driven by the Tent Map and the Logistic Map

Recall the Driven IFS method for representing data. We take the tent and logistic maps as the generators of our examples.

Here are some examples with the logisitc and tent maps, for the indicated s.

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 = 1.7. A wider range of values is produced, and more combinations of bins are visited. Note some restrictions: 1 -> 1, 2 -> 2, and 4 -> 4 do not occur. s = 1.8. Now 1 -> 1 is allowed, and more of the regions are filled.

Here are some animations of how the driven IFS varies with the s parameter of the logistic and tent maps.