Selected Images from The Optiverse

The following images are stills taken from The Optiverse, a video by John Sullivan, George Francis, and Stuart Levy, about the minimax sphere eversion.

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Transparent eversions

These images show the 2-fold eversion in an early "gastrula" stage, at a stage between the creation of the first and second double curves, and finally almost at the halfway stage.

These images all show the 2-, 3-, 4-, and 5-fold eversions in the upper left, lower left, upper right, and lower right cornerse, respectively. First we see an early stage, with p fingers growing in the p-fold everion. Next we see an intermediate stage when the fingers have mostly overlapped. Finally we see the four halfway models. For p odd, these are doubly covered projective planes.