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 = 1.4. The bands have almost merged. s = 1.5. The bands have merged, but there is little diffrence between this and the previous picture.

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

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