Midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. Bresenham's circle algorithm is derived from the midpoint circle algorithm. wikipedia 
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I began construction of an observable to get my head around the algorithm. observable
The exploration was motivated by questions on the path from Your NaN is My Zero to Test Counting With Method and on to Dance Another Step, though this algorithm fails to answer Ward's question.
Discussion about accumulation of errors and feedback loops remind me of talking with Ralph about Project X at Bell Labs in WWII. See Origin of Digits