As stated on the previous page, many permutations can begin to crop, so the cosmos seems to have variety built into it’s system.
Lets continue on to the 7x7 grid.
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
Specific Constant = 7
We need to add seven numbers to
attain our “Grid Constant” = 175
So, a 7x7 grid has a spefic
constant of 7 and a grid constant of 175









































































































































































































































































































































































































































































































































































The “Zero Sum Variable” is now 10.
43+37+31+25+19+13+7=175
1+9+17+25+33+41+49=175
22+23+24+25+26+27+28=175
4+11+18+25+32+39+46=175
8+2+31+25+19+48+42=175
36+44+17+25+33+6+14=175
3+5+24+25+26+45+47=175
15+29+18+25+32+21+35=175
10+12+18+25+32+38+40=175
16+30+24+25+26+20+34=175
We
have consumed all the numbers in this grid while respecting symmetry.
At this point we could go on to an 8x8 grid, but there are some
interesting patterns that are emerging using the previous grids…
The first and most obvious is the diagonal pattern. Which
exists for every grid, regardless of the number. The second pattern
that will be a constant is the veritical and horizontal middle. They
come in two shapes:
For odd numbers: 

As you can see taking the middle point on the x and y axis, you get two straight lines thata add up to a specific number.
For even numbers: 

For even numbers, we need to do a small jump in the middle... to accomplish the task. And so the saying, even numbers are divisible by 2.
Lets recap all the shapes into a reference table:





SPECIFIC CONSTANT 
GRID CONSTANT 
ZERO SUM GRID 
2x2 GRID 
2 
5 
2 
3x3 GRID 
3 
15 
4 
4x4 GRID 
4 
34 
4 
5x5 GRID 
5 
65 
8 
6x6 GRID 
6 
111 
8 
7x7 GRID 
7 
175 
10 
Finding patterns is all fine and dandy, but what does all
this mean from an analytical point of view? At the current time of
writing this paper, probably not much.
But, I do believe that
some if not all of this can be applied to chemistry in the way and
possible combination of elements, in information technology pattern
recognition and artificial intelligence, as well as how we look at
the universe and the fabric of space.
And the hunt for more patterns continues with the infamous 8x8 grid…
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
Specific Constant = 8
We need to add seven numbers to
attain our “Grid Constant” = 260
So, a 8x8 grid has a spefic
constant of 8 and a grid constant of 260
Looking for the least patterns to this grid resulted in a number I was not expecting … 9. Let me show you the patterns… they are quite interesting.
















































































































































































































































































































































































































































































































































































































































Lets double check that we have used all the numbers in this
particular grid to get these 9 shapes
57+50+43+36+29+22+15+8=260
1+10+19+28+37+46+55+64=260
4+12+20+28+37+45+53+61=260
5+13+21+29+36+44+52+60=260
25+26+27+28+37+38+39+40=260
33+34+35+36+29+30+31+32=260
9+2+7+16+49+58+63+56=260
17+3+6+24+48+62+41+59=260
18+11+14+23+42+51+54+47=260
Yup,
that would be all folks!
This last pattern is unique in it stands alone, while the rest seem to have corresponding shapes. That an 8x8 grid would have a “zero sum” count of 9 shapes is indeed new.
Ultimately we could continue, but at this point, I would like to
build a computer program that does this for me as it is a slow and
tedious process trying to do this with a spreadsheet. :)
If
anyone is interested in this, please contact me.