Movies illustrating the Dehn twists about the rabbit's ears

These movies illustrate the "rabbit trick", i.e. Douady's question of determining the Thurston equivalence class of the topological polynomial obtained by applying a Dehn twist to the rabbit polynomial. The answer is given in the paper Thurston equivalence of topological polynomials, with Volodymyr V. Nekrashevych.

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.

AVI movies

MPG movies

MOV movies