increasing_cyclical.py

from itertools import cycle, islice
import pprint
                
# one cycle of the group
def increasing_cyclical(xs, period, max_width):
    """
    Find the subcycles of an iterable given a depth and breadth.
    period: the depth of the subcycle
    max_width: the breadth of the subcycle
    """
    for x in range(period):
        g = list(islice(cycle(xs), period+x))[x:]
        for y in range(max_width):
            yield list(islice(iter(g), y+1))


# cycle the group forever
def increasing_cyclical(xs, period, max_width):
    while True:
        for x in range(period):
            g = list(islice(cycle(xs), period+x))[x:]
            for y in range(max_width):
                yield list(islice(iter(g), y+1))

                
# Example output:

>>> pprint(list(increasing_cyclical('abcd', 3, 1)))
[['a'], ['b'], ['c']]
>>> pprint(list(increasing_cyclical('abcd', 4, 1)))
[['a'], ['b'], ['c'], ['d']]
>>> pprint(list(increasing_cyclical('abcd', 4, 2)))
[['a'], ['a', 'b'], ['b'], ['b', 'c'], ['c'], ['c', 'd'], ['d'], ['d', 'a']]
>>> pprint(list(increasing_cyclical('abcd', 4, 3)))
[['a'],
 ['a', 'b'],
 ['a', 'b', 'c'],
 ['b'],
 ['b', 'c'],
 ['b', 'c', 'd'],
 ['c'],
 ['c', 'd'],
 ['c', 'd', 'a'],
 ['d'],
 ['d', 'a'],
 ['d', 'a', 'b']]
>>> pprint(list(increasing_cyclical('abcd', 4, 4)))
[['a'],
 ['a', 'b'],
 ['a', 'b', 'c'],
 ['a', 'b', 'c', 'd'],
 ['b'],
 ['b', 'c'],
 ['b', 'c', 'd'],
 ['b', 'c', 'd', 'a'],
 ['c'],
 ['c', 'd'],
 ['c', 'd', 'a'],
 ['c', 'd', 'a', 'b'],
 ['d'],
 ['d', 'a'],
 ['d', 'a', 'b'],
 ['d', 'a', 'b', 'c']]
>>>