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 = 3.8. Chaos again, but there's certainly some underlying order. s = 3.825. Some small, but definite, changes between this and s = 3.8.

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

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