The video clips illustrating complex dynamics typically have a few MB and a duration of about 30s. They were produced with FFmpeg, combining images made with Mandel. For each video, two links are given: clicking play will open the video in a new browser tab or window. Or right-click to save the file to your hard disk, and open it with a video player. Clicking show opens a small pop-up box to play the video in reduced size.

Symmetric rational maps

Quadratic rational maps fc(z) = (z2 + c) / (1 + cz2) form the family of symmetric maps, since they commute with the inversion z ↦ 1/z. The videos illustrate applications of the Thurston algorithm to construct these maps from polynomials. The visualization of mating is based on the Buff–Chéritat approach to slow mating.

Mating and anti-mating

Definitions of mating and anti-mating are given here. Relation of P ∐ P and P ∏ P ...

Phase space videos and more locus videos are under construction ...

also non-self and ref mixing

Deformation of M to the loci of self-matings and and self-anti-matings: play — show.
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Locus of the 1/3-limb mated and anti-mated with itself: play — show.
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The 1/4-vein mated and anti-mated with itself: play — show.
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Lattès maps

In general divergent; see the joint paper [B6] with Arnaud Chéritat and the poster from the conference celebrating John Milnor.

1/12 v 5/12 (unsymmetric): play — show.
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1/4 v 1/4 convergent: play — show.
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53/60 v 29/60 : play — show.
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3/14 v 3/14 : play — show.
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1/6 v 1/6 : play — show.
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Chebyshev maps

For a Chebyshev map ya(z) = (-z2 + a + 2) / (z2 + a), we have ∞ ↦ -1 ↦ 1, and 1 is fixed. The Petersen transformation sends fc(z) and f1/c(z) to the same Chebyshev map, and especially P ∐ P and P ∏ P to P ∐ T with T(z) = z2 - 2.

other possibilities, here veins through period 3, when equal

veins ...: play — show.
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veins ...: play — show.
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