Add two 4-D arrays in Python
Firstly, code that looks like:

foo = 0
while foo &lt; bar:
    ...  # foo doesn't change here
    foo += 1


is a bad sign. In Python, this can immediately be simplified, using range, to:

for foo in range(bar):
    ...




Secondly, hard-coding the shape of your "arrays" everywhere (having the literals 51, 150 and 207 in the code itself), referred to as "magic numbers", is poor practice in every programming language. These are the lengths of each sub-list, so should be calculated as needed using len(...). This makes the code more flexible; it can now be easily applied to add arrays of other sizes. it's also slightly awkward to hard-code the depth of the addition (i.e. that it only handles four-dimensional arrays).



Thirdly, however, code like:

for index in range(len(sequence)):
    element = sequence[index]
    ...


is generally better replaced with:

for element in sequence:
    ...


where you need the index too, you can use enumerate, and where you need to iterate over multiple iterables you can use zip; Python has lots of handy functions for dealing with iterables (see also itertools).



Fourthly, when you have a loop appending to a list, it's usually more efficient to replace it with a "list comprehension". For example:

foo = []
for bar in baz:
    foo.append(bar)


can be replaced by:

foo = [bar for bar in baz]




Finally, however, this is totally trivial if you switch to numpy, which is extremely helpful for manipulating arrays: 

&gt;&gt;&gt; import numpy as np
&gt;&gt;&gt; arr1 = np.random.randint(1, 10, (1, 51, 150, 207))
&gt;&gt;&gt; arr2 = np.random.randint(1, 10, (1, 51, 150, 207))
&gt;&gt;&gt; arr1 + arr2  # wasn't that easy!
array([[[[11, 13, 14, ...,  9, 14,  8],
         [15,  4, 10, ..., 14, 10, 16],
         [11, 11,  9, ...,  4,  9,  9],
         ..., 
         [17, 10, 14, ..., 10, 12, 12],
         [12, 11, 14, ...,  7,  8,  8],
         [ 9, 11,  6, ...,  3, 11,  8]],

        [[10, 15, 16, ..., 11, 16, 10],
         [17, 17,  8, ...,  8,  7,  8],
         [11,  7,  2, ..., 16, 11,  5],
         ..., 
         [15, 10, 16, ..., 16, 13,  9],
         [15,  8,  7, ..., 13,  5,  6],
         [ 4,  5, 10, ...,  7, 10, 10]],

        [[11, 10,  4, ..., 10,  7, 11],
         [12,  3, 14, ..., 11, 12, 12],
         [ 6, 11, 16, ..., 14,  9, 12],
         ..., 
         [18, 10, 11, ..., 13, 14,  9],
         [11, 11, 10, ...,  9, 13, 12],
         [10, 10, 10, ..., 12, 14,  8]],

        ..., 
        [[16, 11, 12, ..., 13, 13,  9],
         [ 7, 15, 10, ...,  9, 11,  5],
         [ 5, 11, 14, ..., 14,  4, 11],
         ..., 
         [15, 13,  6, ..., 17,  6, 10],
         [ 9, 12,  7, ...,  7, 17, 11],
         [12,  9, 10, ...,  4,  9,  5]],

        [[15, 12, 10, ...,  5, 12, 15],
         [17, 14, 15, ..., 13, 11,  8],
         [13, 10, 10, ...,  8,  4,  8],
         ..., 
         [12,  9, 10, ...,  9,  7, 12],
         [13, 12, 17, ...,  7, 13, 10],
         [13,  6,  8, ..., 15, 13,  7]],

        [[ 9,  8,  8, ...,  6, 10,  2],
         [ 9, 15, 14, ..., 14,  4,  5],
         [ 3, 12, 12, ...,  5, 10, 14],
         ..., 
         [ 6, 11, 15, ..., 11,  4, 15],
         [ 4, 12, 14, ..., 12, 11,  9],
         [10,  3,  5, ...,  5,  7, 10]]]])