Can Ulam's Spiral Theory Be Enhanced with a Double Spiral Approach?

[qwantum_phlux]

To begin i am by no means a machine for converting coffee into theoroms (a mathematician) by do like to dabble. i was lookin over ulam's theory of plotting real integers in a spiral fom:

7 6 5
8 1 4
9 2 3
10 11 ...

in an attempt to find a pattern in prim numbers...
i know my idea may be invalid on the account of imaginary primes... but i was wondering if anyone had tried the same but with a double spiral starting with 0 in the center and negative integers:
-8 -7 -6 -5
-9 2 1 -4
... 3 0 -3 ...
4 -1 -2 9
5 6 7 8
my formatting isn't the greatest, but you get the idea. if the idea is invalid feel free to shoot me down, and if not could one suggest an algorithm to load the integers into and array in a this spiral pattern so i can load a large plot to compare...(im attempting to write a program).

 

[qwantum_phlux]

-8 -7-6 -5
-9 2 1 -4
3 0 -3
4 -1 -2 9
5 6 7 8
(format fix)

 

[qwantum_phlux]

-7-6-5
2 1 -4
3 0 -3
4-1-2
5 6 7
{final attempt}