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.

We use equal-size bins.

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.

Return to Deterministic Chaos.

	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.