#MCell 2.0
#GAME Generations
#RULE 345/2/4
#BOARD 400x400
#SPEED 50
#WRAP 0
#CCOLORS 4
#D Guns of period less than 4 are clearly impossible.
#D But this construction shows that all higher periods are possible.
#D The construction does not deal with periods 4 and 5, for which simpler
#D guns exist.
#D 
#D To construct a gun of period n > 5 do the following:
#D   Choose a positive integer m such that 6(m+1) is a multiple of n.  For example, you can
#D   always choose m=n-1, but a smaller choice of m is possible if n is a multiple of 2 or 3.
#D   Make the still life constisting of m 5-cell crosses joined in a row.  Place 6(m+1)/n
#D   3-cell "runners" around the edge of this still life, spaced n generations apart.
#D   Add the other two still lifes in the manner shown in the examples.
#D 
#D The given examples illustrate periods 6, 10,  15, and an irregular gun.
#D 
#D Stephen Silver, 10 May 1999
#L 14.A..A$13.6A$12.AA3.A$11.AA4.A$10.AA5.AA$11.A5.A$6.A4.A5.A$5.A.B..9A$
#L 3.C3AC3.A..A..A$3.B.A$4.A$$.A6.A4.A$15A$.A..A..A..A..A11$5.A$4.4A$5.A.
#L B6.A..A$3.C.A.C5.6A$3.B3A5.AA3.A$3.A.A5.AA4.A$5.A4.AA5.AA$4.3A4.A5.A$
#L 5.A5.A5.A$5.A4.9A$4.3A4.A..A..A$5.A.A$5.CB$$.A6.A4.A$15A$.A..A..A..A..
#L A15$5.A$4.3A$5.A8.A..A$5.A.A5.6A$4.3AB4.AA3.A$5.A.C3.AA4.A$3.C.A4.AA5.
#L AA$3.B3A4.A5.A$3.A.A5.A5.A$5.A4.9A$4.3A4.A..A..A$5.A3$.A6.A4.A$15A$.A
#L ..A..A..A..A11$5.A$4.3A$3.C.A$3.B.A$3.4A$5.A8.A..A$5.A7.6A$4.3A5.AA3.A
#L $3.C.A5.AA4.A$3.B.A4.AA5.AA$3.4A4.A5.A$5.A5.A5.A$5.A4.9A$4.3A4.A..A..A
#L $3.C.A$4.BA$$.A6.A4.A$15A$.A..A..A..A..A