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Errors

Further disscussion and code example can be found in another question.

Errors

Update You could go a step further, by precalculating all posible paths for several steps.

Outlook

After understanding what your code is intended to do, I think your for-loop over all paricles is not doing what you intend.

Also, you only start particles an the upper and left border?

The name arr is an example for a bad name, because it hints to "array" (thus it was hard to spot the mistake above). Better would be samething like area.

Precalculation

You could go a step further, by precalculating all posible paths for several steps.

Outlook - binomial distribution and minimal distance matrix

After understanding what your code is intended to do, I think your for-loop over all paricles is broken.

Also, you only start particles at the upper and left border?

The name arr is an example for a bad name, because it hints to "array" (thus it was hard to spot the mistake above). Better would be samething like area. Or use h and w (personally I would prefer to name thus as height and width; thats easier to read in most cases)

Errors

After understanding what your code is intended to do, I think your for-loop over all paricles is not doing what you intend.

First:

pos = np.random.randint(0, len(arr))  # will set pos to 0 or 1
# should be:
pos = np.random.randint(0, arr[0])
# or better
random_pos_x = np.random.randint(0, arr[0])
random_pos_y = np.random.randint(0, arr[1])

Also, you only start particles an the upper and left border?

walk(pos,-1,canvas)  # why -1?
...
walk(-1,pos,canvas)  # why -1?

# should be:
walk(random_pos_x ,arr[1]-1, canvas)
walk(arr[0]-1, random_pos_y, canvas)

The name arr is an example for a bad name, because it hints to "array" (thus it was hard to spot the mistake above). Better would be samething like area.