A Sandpile class created in Python to simplify the calculations explained in this Numberphile video https://www.youtube.com/watch?v=1MtEUErz7Gg

sandpile.py

'''Sandpile class'''

class Sandpile:
    '''A mathmatical sandpile.'''

    def __init__(self, pile, cols, rows):
        self.cols = cols
        self.rows = rows

        self.pile = pile

    def __str__(self):
        string = ""
        for i, item in enumerate(self.pile):
            string += str(item) + " "
            if (i + 1) % self.cols == 0:
                string += "\n"
        return string

    def __add__(self, other):
        if self.cols == other.cols and self.rows == other.rows:
            pile = self.pile.copy()
            for item in enumerate(pile):
                pile[item[0]] += other.pile[item[0]]
            return Sandpile(pile, self.cols, self.rows)
        else:
            raise ValueError("Size of the piles is different. Must be same size to add.")

    def __sub__(self, other):
        raise ArithmeticError("Cannot subtract sandpiles.")

    def __pow__(self, exp):
        pile = self.pile.copy()
        for item in enumerate(pile):
            pile[item[0]] = pile[item[0]] ** exp
        return Sandpile(pile, self.cols, self.rows)


    def topple(self):
        '''This method topples the sandpile.'''
        i = 0
        while i < len(self.pile):
            if self.pile[i] >= 4:
                coords = self.get_coords(i)

                self.distribute(coords)

                i = 0
                continue
            i += 1

        return self

    def distribute(self, coords):
        '''This function ditributes the 'sand' in the spot specified.'''
        cell = self.get_index(coords)
        times_four = self.pile[cell] // 4

        self.pile[cell] -= 4 * times_four

        for neighbor in Sandpile.get_neighbors(coords):
            index = self.get_index(neighbor)
            if index is not None:
                self.pile[index] += times_four

    def get_coords(self, index):
        '''Gets an index and returns a tuple as Coords.'''
        row = index // self.rows
        col = index - (row * self.rows)

        return (col, row)

    def get_index(self, coords):
        '''Gets coords and returns a index number.'''
        col = coords[0]
        row = coords[1]
        if col < 0 or row < 0 or col > self.cols - 1 or row > self.rows - 1:
            return None
        return col + row * self.cols

    @staticmethod
    def get_neighbors(coords):
        '''This functions returns the neighbors of the passed spot.'''
        col = coords[0]
        row = coords[1]
        neighbors = [(col - 1, row), (col, row + 1), (col + 1, row), (col, row - 1)]

        return neighbors