72 lines
1.6 KiB
Python
72 lines
1.6 KiB
Python
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'''Cantor set – strings as both model and display.'''
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from itertools import (chain, islice)
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# cantorLines :: Int -> String
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def cantorLines(n):
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'''N levels of cantor segmentation,
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obtained and displayed in the
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form of lines of block characters.
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'''
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return '\n'.join(
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[''.join(x) for x in islice(
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iterate(cantor)(
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[3 ** (n - 1) * '█']
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), n
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)]
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)
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# cantor :: [String] -> [String]
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def cantor(xs):
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'''A cantor line derived from its predecessor.'''
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def go(s):
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m = len(s) // 3
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blocks = s[0:m]
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return [
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blocks, m * ' ', blocks
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] if '█' == s[0] else [s]
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return concatMap(go)(xs)
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# MAIN ----------------------------------------------------
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# main :: IO ()
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def main():
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'''Testing cantor line generation to level 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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return lambda xs: list(
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chain.from_iterable(map(f, xs))
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)
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# iterate :: (a -> a) -> a -> Gen [a]
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def iterate(f):
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'''An infinite list of repeated
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applications of f to x.
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'''
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def go(x):
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v = x
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while True:
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yield v
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v = f(v)
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return lambda x: go(x)
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# MAIN ---
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if __name__ == '__main__':
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main()
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