Talk:Abelian sandpile model
optimizations ?
the figures are 8xtimes symmetric like drawing a circle. But how to calculate the generating triangle. See 16->
00100 02120 11011 02120 00100 the origin is the starting point of the sandpile. is rotated and mirrored of X20 011 mirrored at main diagonal 100 120 011 rotated 3 times by 90° around the origin.
A more readable Python solution.
This solution is more interactive, as it can also be used in imports on a Python console; plus, it is more readable. <lang python> def make_area(x, y): global area area = [[0]*x for _ in range(y)] return area
def make_sandpile(loc, height): global area loc=list(n-1 for n in loc) x, y = loc
try: area[y][x]+=height except IndexError: pass
def run(): global area while any([any([pile>=4 for pile in group]) for group in area]): for y_index, group in enumerate(area): y = y_index+1
for x_index, height in enumerate(group): x = x_index+1
if height < 4: continue
else: make_sandpile((x-1, y), 1) make_sandpile((x+1, y), 1) make_sandpile((x, y-1), 1) make_sandpile((x, y+1), 1) make_sandpile((x, y), -4)
def show_area(): global area display = [' '.join([str(item) for item in group]) for group in area] [print(i) for i in display]
if __name__ == '__main__':
area = make_area(10, 10)
print('\nBefore:')
show_area()
make_sandpile((5, 5), 64); run()
print('\nAfter:')
show_area()
</lang>
Output: <lang> Before: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
After: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 1 2 2 2 2 2 1 0 0 0 2 2 2 0 2 2 2 0 0 0 1 2 2 2 2 2 1 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 </lang>