We describe how to approximate fractal transformations generated by a one-parameter family of dynamical systems W: [0, 1] → [0, 1] constructed from a pair of monotone increasing diffeomorphisms Wi such that W-1i : [0, 1] → [0, 1] for → = 0, 1. An algorithm is provided for determining the unique parameter value such that the closure of the symbolic attractor is symmetrical. Several examples are given, one in which the Wi are affine and two in which the Wi are nonlinear. Applications to digital imaging are also discussed.
History
Preferred citation
Harding, B. (2019). Symmetric itinerary sets: Algorithms and nonlinear examples. Bulletin of the Australian Mathematical Society, 100(1), 109-118. https://doi.org/10.1017/S0004972719000297