75 lines
1.6 KiB
Python
75 lines
1.6 KiB
Python
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'''Cantor set – separating model from display'''
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from functools import (reduce)
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import itertools
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# cantor :: [(Bool, Int)] -> [(Bool, Int)]
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def cantor(xs):
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'''A Cantor segmentation step.'''
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def go(tpl):
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(bln, n) = tpl
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m = n // 3
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return [
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(True, m), (False, m), (True, m)
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] if bln and (1 < n) else [tpl]
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return concatMap(go)(xs)
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# cantorLines :: Int -> String
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def cantorLines(n):
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'''A text block display of n
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Cantor-segmented lines.
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'''
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m = n - 1
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repeat = itertools.repeat
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return '\n'.join(
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[showCantor(x) for x in (
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reduce(
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lambda a, f: a + [f(a[-1])],
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repeat(cantor, m),
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[[(True, 3 ** m)]]
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)
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)]
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)
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# showCantor :: [(Bool, Int)] -> String
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def showCantor(xs):
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'''A text block display of a list of
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Cantor line segments.
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'''
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return ''.join(
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concatMap(lambda tpl: tpl[1] * ('█' if tpl[0] else ' '))(
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xs
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)
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)
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# main :: IO ()
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def main():
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'''Testing to depth 5'''
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print(
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cantorLines(5)
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)
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# GENERIC -------------------------------------------------------------
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# concatMap :: (a -> [b]) -> [a] -> [b]
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def concatMap(f):
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'''A concatenated list over which a function has been mapped.
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The list monad can be derived by using a function f which
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wraps its output in a list,
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(using an empty list to represent computational failure).'''
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chain = itertools.chain
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return lambda xs: list(
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chain.from_iterable(map(f, xs))
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)
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# MAIN ---
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if __name__ == '__main__':
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main()
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