6.D.6. IFS Driven by Dynamical Systems

The s = 3.732 Logistic Map

The left picture is the IFS driven by the s = 3.723 logistic map; the right picture is generated by a random IFS with the s = 3.732 logistic map forbidden pairs imposed.

Every empty subsquare of the right picture has address contaning one of the pairs 11, 12, 13, 21, 22, 23, 32, or 44.

Consequently, the left picture has some empty subsquares that are not consequences of the empty pairs. In this sense, the left picture is more complex than the right.

IFS driven by the s = 3.732 logistic map Random IFS with the s = 3.732 forbidden pairs imposed

In examples such as the s = 4.0 logistic map, the driven IFS is completely determined by the forbidden pairs.

This is because partitioning the range [0, 1] into four equal intervals is a Markov partition.

Return to IFS Driven by Dynamical Systems.


IFS driven by the s = 3.732 logistic map		Random IFS with the s = 3.732 forbidden pairs imposed