collatz.py

import matplotlib.pyplot as plt

from collections import Counter

MAX_I = 200

becomes_even = 0
becomes_odd = 0

# for i in range(1, MAX_I, 2):
#     result = (i * 3 + 1) / 2
#     if result % 2 == 0:
#         becomes_even += 1
#     else:
#         becomes_odd += 1


# for i in range(0, MAX_I, 2):
#     if (i / 2) % 2 == 0:
#         becomes_even += 1
#     else:
#         becomes_odd += 1


def get_full_pattern(n, combine=True, stop_on_dip=False):
    seen = set()
    pattern = ""
    initial = n
    while True:
        seen.add(n)
        if n % 2 == 0:
            pattern += "X"
            n = n / 2
        else:
            pattern += "O"
            if combine:
                n = (n * 3 + 1) / 2
            else:
                n = n * 3 + 1
        if n in seen or stop_on_dip and n < initial:
            break
    return pattern


def get_collatz_pattern(n, depth, combine=True):
    pattern = ""
    for _ in range(depth):
        if n % 2 == 0:
            pattern += "X"
            n = n / 2
        else:
            pattern += "O"
            if combine:
                n = (n * 3 + 1) / 2
            else:
                n = n * 3 + 1
    return pattern


def checker():
    BLOCKS_TO_CHECK = 1
    DEPTH = 8

    for DEPTH in range(1, 15):
        BLOCK_LENGTH = 2**DEPTH

        patterns = []
        for i in range(BLOCK_LENGTH * BLOCKS_TO_CHECK):
            pattern = get_collatz_pattern(i, DEPTH)
            full_pattern = get_full_pattern(i)
            # print(f"{i}\t{pattern}\t{full_pattern}")
            patterns.append(pattern)

        first_block = patterns[:BLOCK_LENGTH]

        depth_pattern = ""
        for pattern in first_block:
            depth_pattern += pattern[DEPTH - 1]
        print(DEPTH, Counter(depth_pattern))

        # print(f"{first_block} repeats infinitely")
        assert patterns == first_block * BLOCKS_TO_CHECK


def get_full_map(width, height, **kwargs):
    collatz_map = []
    for y in range(height):
        row = [
            1 if symbol == "O" else 0
            for symbol in get_collatz_pattern(y, width, **kwargs)
        ]
        collatz_map.append(row)
    # return list(zip(*collatz_map))
    return collatz_map


def get_actual_map(width, height, **kwargs):
    collatz_map = []
    for y in range(height):
        row = [
            [0, 255, 0, 255] if symbol == "O" else [255, 0, 0, 255]
            for symbol in get_full_pattern(y, **kwargs)
        ][:width]

        if len(row) < width:
            row += [[0, 0, 0, 0]] * (width - len(row))

        collatz_map.append(row)
    return collatz_map


# actual_map = get_actual_map(200, 2056)
# shortcut_map = get_full_map(100, 128, combine=False)
actual_optimized_map = get_actual_map(200, 2056, stop_on_dip=False)
full_map = get_full_map(200, 2056)

fig, (ax2, ax3) = plt.subplots(1, 2, sharex=True, sharey=True)

# ax1.imshow(actual_map)
ax2.imshow(actual_optimized_map)
ax3.imshow(full_map)

plt.show()