Essential singularity of exp(1/z)

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Near an essential singularity, an analytic function takes on all possible values infinitely many times except possibly one.

This is called Picard's (greater) theorem!

This animation zooms in on the essential singularity of exp(1/z) about z → 0.
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Very pretty! What's up with the red spot near the origin? 🤨

nzuckman