Generate aperiodic MOS scales

[frostburn]

https://en.xen.wiki/w/Hypercubic_billiard_word

[frostburn]

The parameters would be the sizes of large and small steps and the ratio of large steps to small steps with some sane defaults for the initial state of the "billiard ball".

If we want to generalize this package to larger varieties the parameters would be the sizes of steps and an array of proportionalities between them.

[frostburn]

0.5° 🌜 — Today at 5:24 PM
my billiard-related Python code, for comparison, is:

def collisions(alphabet: Sequence[str],
               vel: Sequence[Fraction],
               start_pos: Sequence[Fraction]) -> Iterator[str]:
    dim = len(alphabet)
    if dim == 0:
        raise ValueError('alphabet should be nonempty')
    if len(vel) != dim:
        raise ValueError('len(vel) should equal len(alphabet)')
    if len(start_pos) != dim:
        raise ValueError('len(start_pos) should equal len(alphabet)')
    if any(v <= 0 for v in vel):
        raise ValueError('vel should contain positive numbers')
    if not all(0 <= x < 1 for x in start_pos):
        raise ValueError('start_pos should contain numbers 0 <= x < 1')

    # we’ll decrement to 0 with unit velocity in each dimension
    pos = [(1 - x) / v for x, v in zip(start_pos, vel)]
    start_pos = pos.copy()
    bounds = tuple(1 / v for v in vel)
    while True:
        times = [(x, j) for j, x in enumerate(pos)]
        times.sort()
        t0 = times[0][0]  # the first imminent collision time
        for t, j in times:
            if t == t0:
                pos[j] = bounds[j]
                # in a tie, different j should go in increasing order
                yield alphabet[j]
            else:
                pos[j] -= t0
        if pos == start_pos:
            return  # cycle

should be fully general due to start_pos
also usually the first velocity is okay to be equally 1