ne of the ingredient of the Morris-Construction is "Tweaking", something that is difficult to program. Yet the procedure
can be implemented and tweaks can be added in due time. I have still not decided the format of the tweaker, so the table
below holds the implemented Morris-Construction uptill now.
|The Morris Construction|
The Morris construction is like the "Latin Prescription" and the "KnightJump Procedure" a parametrizable method|
Basically a line of digits is copied throughout the square either normally or complemetairy.
Below the morris construction thus far implemented!
perm(0..m-1)l denotes a permutation of l of the m digits (complementairy exclusive)
The basic format of the construction
||the first permutation is placed in the high components first row
and complemented into the second row
these two lines are repaeted to fill up the high component.
simularly the second permatation is placed in the low components first column
complemented into the second column
and repeated to fill up the entire low component.
The second format of the construction
Half the digits are mentioned and their complements are copied into the second half
|this form merely shortens the basic form the basic format follows from:
perm(0..m-1)m[i] = perm(0..m-1)m/2[i] i = 0 .. m/2 - 1
perm(0..m-1)m[m/2 + i] = m - 1 - perm(0..m-1)m/2[i] i = 0 .. m/2 - 1
Note: the two permutation forms can be combined
's iteration of all order 8 Franklin Square allowed us to investigate these. To me it turns out these are best viewed as having three radix 4 components in stead of two radix 8 components, the spreadsheet Order8Franklin.xlsx exploits these and using excell 2007 conditional formatting shows features of selected squares. The spreadsheet holds a full listing of 576 squares with all component quaters solid order 4 latin squares, a selection of the 1440 "magic" as well as all 4320 Franklin squares Perter Loly found in a normalized listing. Component permutation over the three components show squares that are and that are not in the squares listed by Peter Loly note that this is the first time I have used three components used in squares, the conditions resulting in Loly's listing I haven't analysed with respect too this novel type oof decomposition.