Created
January 16, 2017 16:06
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Python code to toy around with Sandpiles, as described on Numberphile: https://www.youtube.com/watch?v=1MtEUErz7Gg
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| #!/usr/bin/env python | |
| """Computations on Sandpiles. | |
| See: https://www.youtube.com/watch?v=1MtEUErz7Gg | |
| """ | |
| import numpy as np | |
| class Sandpile: | |
| nums = np.zeros((3, 3), int) | |
| def __init__(self, nums: np.ndarray=None): | |
| if nums is not None: | |
| self.nums = np.array(nums, int) | |
| def __repr__(self) -> str: | |
| return 'Sandpile:\n%s' % self.nums | |
| def __add__(self, other: 'Sandpile') -> 'Sandpile': | |
| """Adds two sandpiles together.""" | |
| intermed = Sandpile(self.nums + other.nums) | |
| intermed.topple() | |
| return intermed | |
| def topple(self): | |
| while True: | |
| to_topple = self.nums > 3 | |
| if not to_topple.any(): | |
| break | |
| for rowidx, row in enumerate(to_topple): | |
| for colidx, should_topple in enumerate(row): | |
| if not should_topple: continue | |
| self.nums[rowidx][colidx] -= 4 | |
| for drow, dcol in ((-1, 0), (0, -1), (1, 0), (0, 1)): | |
| to_row = rowidx + drow | |
| to_col = colidx + dcol | |
| if not 0 <= to_row < self.nums.shape[0]: continue | |
| if not 0 <= to_col < self.nums.shape[1]: continue | |
| self.nums[to_row][to_col] += 1 | |
| print('After toppling: %s' % self) | |
| if __name__ == '__main__': | |
| # a = Sandpile([[2, 2, 2], [0, 0, 0], [0, 0, 0]]) | |
| # b = Sandpile([[2, 2, 3], [1, 0, 1], [1, 1, 1]]) | |
| # a = Sandpile([[2, 2, 2], [2, 2, 2], [2, 2, 2]]) | |
| # a = Sandpile([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) | |
| # b = Sandpile([[3, 3, 3], [3, 1, 3], [3, 3, 3]]) | |
| # b = Sandpile([[2, 1, 2], [1, 0, 1], [2, 1, 2]]) | |
| a = Sandpile([[2, 2], [2, 2]]) | |
| b = Sandpile([[1, 2], [0, 2]]) | |
| import doctest | |
| doctest.testmod() | |
| print('a = %s' % a) | |
| print('b = %s' % b) | |
| print('a + b = %s' % (a + b)) |
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