Images of the unit circle under variously truncated function ( series for inverse conformal map between complement of unit disc and complement of set).

The most accurate curve is truncated to 500 terms, but is still very far from the boundary of the set, especially around cusps. The series is very slow to converge.


I made a diagram based on one by Adam Majewski on wikicommons. Turns out the `betaF` code on the mu-ency page is way faster than the earlier code on the page. This image with 1000 terms calculated in a fraction of the time of 500 terms used in the previous post. Seems to take roughly O(n log n) space (discounting the growth of the numbers stored..).

I'm using my memo-sqlite package to memoize the series coefficients in a database, persisted between program invocations, so I don't have to wait 30mins each time.

Then I convert and pack the list of Rational from the db into an unboxed Vector Double, for faster series evaluation at each point of the curve (using Horner's rule).


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