6.D.6. IFS Driven by Dynamical Systems

Recall the method of driving an IFS by a time series. To develop some practice in interpreting these graphics, we drive the IFS with the tent map and the logisitc map.

First, we drive an IFS by the s = 4 Logistic map. We see the dirven IFS is very far from filling up the unit square. To begin to understand this picture, we determine the empty length 2 addresses for the s = 4 Logistic map. Now drive an IFS randomly, except forbid the pairs that are forbidden in the s = 4 logistic map. We get the same picture as with the s = 4 logistic map. Another way to see this is to apply the deterministic IFS rules, but imposing the forbidden combinations. Now we drive an IFS by the s = 2 Tent map. Note the differences between this driven IFS and that of the s = 4 logistic map. For comparison we drive an IFS by the s = 3.732 Logistic map. Now drive an IFS randomly, except forbid the pairs that are forbidden in the s = 3.732 logistic map. Unlike with the s = 4 logistic map and the s = 2 tent map, here the pictures are different.

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