Well, q transformed by a unit disk automorphism. That includes rotations. But more interesting effects from translations.
plotting Jacobian theta functions on z as q is moved contnuously SL(2,Z)/Mobius transformed produces interesting results @tomcuchta
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https://math.stackexchange.com/questions/1367282/automorphisms-of-the-unit-disk … I will post an example later.
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We need terminology for the phalanges? Here's a root and here's its phase contrail?
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