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Question: in the code snippet bleow, what does the result stream, rs, approximate?

from itertools import count, ifilter, islice, izip
from random import random as xy
    
pt = lambda: (xy(), xy())
on = ifilter(lambda n: abs(complex(*pt())) < 1., count(1))
rs = (4. * j / i for i, j in izip(on, count(1)))

The code isn’t wilfully obscure but I’ll admit it’s unusual. Although written in a functional style, the source of the stream, pt, is utterly impure, generating a sequence of random results: it sprinkles points in a unit square. Despite this random input the results stream always tends to the same value. Well, in theory it should!

Incidentally, applying abs() to a complex number returns the modulus of that number: it’s easier than math.sqrt(x * x + y * y). And I’m counting from 1, not 0, to avoid dividing by zero.

>>> abs(3+4j)
5.0
>>> pt = 5, 12
>>> abs(complex(*pt))
13.0

Here’s a picture of a round pie on a square baking tray being dusted with sugar.