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#Post#: 35--------------------------------------------------
a method to create symmetric closed magic knight tours on 4m*4n
rectangles
By: gsgs Date: March 13, 2024, 11:41 am
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here is a file with 15 of these 4ssy-tours , as i called them ,
together with their two generating king-tours :
HTML http://magictour.free.fr/4ssy.l2
they all start on (m/2-2,n) and end on (m/2-1,n-2).
They have 8 parts of equal length and form.
Parts 1 and 2 are created by generating 2m*2n king-tours
part 3 is Sy(part 1) reversed
part 4 is Sy(part 2) reversed
part 4+i is Sxy(part i) for i=1,2,3,4
Sy=horizontal reflection
Sxy=180' - rotation
All but 8 edges have their 2 reflections included in the tour.
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I haven't yet figured out the clear rule
which creates these 4ssy-tours for all rectangles 4m*4n
--------edit 2024-03-15----------------
I think I found a pattern now , how to create a
4m*4n (m>2,n>2) 4-semi0symmetric magic knight tours,
generated by 2m*n double-king tours
2 methods, depending on whether m is odd or even
here is a simple Basic program which prints 4m*4n 4ssy tours :
http:\\magictour.free.fr/AUT9.BAS
see :
[code]
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o-o-o o-o-o
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[/code]
C-program to generate these :
HTML http://magictour.free.fr/4ssymkt.c
------update 2024-03-26-------------
above program now creates 4m*4n symmetric magic knight tours
for m,n>=2
with generating king-tours of length 4mn
----------update 2024-03-28---------------
here a file with the tours upto size 32*32 :
HTML http://magictour.free.fr/sy32.txt
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