RosettaCodeData/Task/One-dimensional-cellular-automata/Python/one-dimensional-cellular-automata-4.py

'''Cellular Automata'''

from itertools import islice, repeat
from functools import reduce
from random import randint


# nextRowByRule :: Int -> [Bool] -> [Bool]
def nextRowByRule(intRule):
    '''A row of booleans derived by Wolfram rule n
       from another boolean row of the same length.
    '''
    # step :: (Bool, Bool, Bool) -> Bool
    def step(l, x, r):
        return bool(intRule & 2**intFromBools([l, x, r]))

    # go :: [Bool] -> [Bool]
    def go(xs):
        return [False] + list(map(
            step,
            xs, xs[1:], xs[2:]
        )) + [False]
    return go


# intFromBools :: [Bool] -> Int
def intFromBools(xs):
    '''Integer derived by binary interpretation
       of a list of booleans.
    '''
    def go(b, pn):
        power, n = pn
        return (2 * power, n + power if b else n)
    return foldr(go)([1, 0])(xs)[1]


# ------------------------- TEST -------------------------
# main :: IO ()
def main():
    '''Samples of Wolfram rule evolutions.
    '''
    print(
        unlines(map(showRuleSample, [104, 30, 110]))
    )


# ----------------------- DISPLAY ------------------------

# showRuleSample :: Int -> String
def showRuleSample(intRule):
    '''16 steps in the evolution
       of a given Wolfram rule.
    '''
    return 'Rule ' + str(intRule) + ':\n' + (
        unlines(map(
            showCells,
            take(16)(
                iterate(nextRowByRule(intRule))(
                    onePixelInLineOf(64) if (
                        bool(randint(0, 1))
                    ) else randomPixelsInLineOf(64)
                )
            )
        ))
    )


# boolsFromInt :: Int -> [Bool]
def boolsFromInt(n):
    '''List of booleans derived by binary
       decomposition of an integer.
    '''
    def go(x):
        return Just((x // 2, bool(x % 2))) if x else Nothing()
    return unfoldl(go)(n)


# nBoolsFromInt :: Int -> Int -> [Bool]
def nBoolsFromInt(n):
    '''List of bools, left-padded to given length n,
       derived by binary decomposition of an integer x.
    '''
    def go(n, x):
        bs = boolsFromInt(x)
        return list(repeat(False, n - len(bs))) + bs
    return lambda x: go(n, x)


# onePixelInLineOf :: Int -> [Bool]
def onePixelInLineOf(n):
    '''A row of n (mainly False) booleans,
       with a single True value in the middle.
    '''
    return nBoolsFromInt(n)(
        2**(n // 2)
    )


# randomPixelsInLineOf :: Int -> [Bool]
def randomPixelsInLineOf(n):
    '''A row of n booleans with pseudorandom values.
    '''
    return [bool(randint(0, 1)) for _ in range(1, 1 + n)]


# showCells :: [Bool] -> String
def showCells(xs):
    '''A block string representation of a list of booleans.
    '''
    return ''.join([chr(9608) if x else ' ' for x in xs])


# ----------------------- GENERIC ------------------------

# Just :: a -> Maybe a
def Just(x):
    '''Constructor for an inhabited Maybe (option type) value.
       Wrapper containing the result of a computation.
    '''
    return {'type': 'Maybe', 'Nothing': False, 'Just': x}


# Nothing :: () -> Maybe a
def Nothing():
    '''Constructor for an empty Maybe (option type) value.
       Empty wrapper returned where a computation is not possible.
    '''
    return {'type': 'Maybe', 'Nothing': True}


# foldr :: (a -> b -> b) -> b -> [a] -> b
def foldr(f):
    '''Right to left reduction of a list,
       using the binary operator f, and
       starting with an initial accumulator value.
    '''
    def g(a, x):
        return f(x, a)
    return lambda acc: lambda xs: reduce(
        g, xs[::-1], acc
    )


# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
    '''An infinite list of repeated
       applications of f to x.
    '''
    def go(x):
        v = x
        while True:
            yield v
            v = f(v)
    return go


# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
    '''The prefix of xs of length n,
       or xs itself if n > length xs.
    '''
    def go(xs):
        return (
            xs[0:n]
            if isinstance(xs, (list, tuple))
            else list(islice(xs, n))
        )
    return go


# unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
def unfoldl(f):
    '''Dual to reduce or foldl.
       Where these reduce a list to a summary value, unfoldl
       builds a list from a seed value.
       Where f returns Just(a, b), a is appended to the list,
       and the residual b is used as the argument for the next
       application of f.
       When f returns Nothing, the completed list is returned.
    '''
    def go(v):
        x, r = v, v
        xs = []
        while True:
            mb = f(x)
            if mb.get('Nothing'):
                return xs
            else:
                x, r = mb.get('Just')
                xs.insert(0, r)
        return xs
    return go


# unlines :: [String] -> String
def unlines(xs):
    '''A single string formed by the intercalation
       of a list of strings with the newline character.
    '''
    return '\n'.join(xs)


# MAIN -------------------------------------------------
if __name__ == '__main__':
    main()