In that paper, we constructed a branched covering on the moduli space of topological polynomials with the same post-critical dynamics as the rabbit polynomial. The movies illustrate the Julia set of these topological polynomials as a point moves in moduli space; they should be thought of as an exploration of a fractal in C^2, which is a bundle over a moduli space fractal (in grey) with fibres the Julia sets of the corresponding topological polynomial.

I wrote in PDF this brief explanation of the movies, with active hyperlinks to them.

These movies are best understood in conjunction with Nekrashevych's preprint An uncountable family of 3-generated groups acting on the binary tree.

The movies are produced by the following C++ code, run on PC/Linux: movie.C, Makefile.

- Following the lifts for generator S of the mapping class group
- Twisting about the generator S of the mapping class group; here in low resolution; here with the moduli and dynamical spaces superposed
- Twisting about the generator T of the mapping class group; here in low resolution
- A zoom on the neighbourhood of the airplane; here in low resolution version
- A zoom on the neighbourhood of the rabbit; here in low resolution
- A Dehn twist applied to a rabbit.
- The Jack Rabbit Slims Twist Contest.

- Twisting about the generator S of the mapping class group; here in low resolution; here with the moduli and dynamical spaces superposed
- Twisting about the generator T of the mapping class group; here in low resolution
- A zoom on the neighbourhood of the airplane; here in low resolution version
- A zoom on the neighbourhood of the rabbit; here in low resolution
- A Dehn twist applied to a rabbit.