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>