Since this is exactly what we don't want to be doing, I created a seperate thread for it. Also I don't have the batter for the other one. I'll probably jump back into the new thread once it is created.
I have devised a way to generate the (e,n,d) coordinates for any d value. This requires new rules. For now, I'm ignoring the x,a,b,c values because they aren't required for this pattern. That said, if we analyze steps of this pattern we may have patterns in x,a,b,c, I just haven't checked yet. I'm still trying to validate if this is the case. Also, for this, you generate (e,n,d,x,a,b,c) values through END(e,n,d) which is posted in my other code dump
(E,N,D,O,T)
Pic related is for D = 6.
On this graph, the +'s indicate a value that was generated by theend(1500) code. The 's indicate a suspected d at that value. Whether or not the 's actually correspond to a cell we can overlook for now, because the pattern seems to hold.
O is the origin cell of a line. Indicated by the integers in the chart (except for the 6,7,8,9 on the line). 0 is the zero origin, 1 is the 1 origin etc.
For each origin cell, the value of T is 0. For the cell on the N+1 row relative to an origin line, we have T = T+1. The T's for O=1 are written for T=6,7,8,9
Now that you can read the values, here are the rules I've discovered:
(-D^2, -D, D, 0, 0) is a valid start record for any D
(e,n,d,o,t) -(e+t^2, n, d, o+t, 0) (to generate origin cell for same row given any cell)
(e,n,d,o,t) -(e+2o, n+1, d, o, t+1) (to get next t) *
(e,n,d,o,t) -(e-2o, n-1, d, o, t-1) (to get prevoius t) *
(e,n,d,o,0) -(e+2ot, n+t, d, o, t) (any t from origin) (basically the same as the two * above)
(e,n,d,o,0) -(e-t^2, n, d, o-t, t) (to generate other cells in row n from t=0) (t<o)
(e,n,d,o,t) -(e+ (2t-1), n, d, o+1, t-1) (to shift from o to o+1)
(e,n,d,o,t) -(e- (2t+1), n, d, o-1, t+1) (shift from o to o-1)
BIG (e,n,d,o,t) -(e+2d-1, n-1, d-1, o,t)
This last equation comes from noticing that the layout of all the D grids is the EXACT SAME, just with a different 0 origin cell.
To factor C, our record (e,n,d,x,1,c) has the correct D already. I suspect that we can generate the correct O and T values from some other method to zip right to our correct cell.