#MCell 2.0
#GAME Generations
#RULE 345/2/4
#BOARD 200x200
#SPEED 50
#WRAP 0
#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,
#D so for completeness these are shown on the right.
#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 two examples.
#D
#D The given examples illustrate the two smallest periods, 6 and 7.
#D
#D Stephen Silver, 10 May 1999
#L ..ABC$..A..A$.6A.A$..A3.AA.B$A.A4.AA.C$BAA5.AA$C.A5.A$..A5.A4.CBA$.10A
#L 3.A25.CB$..A..A..A.B..3A23.AA.A$.ABC3.ABC4.A25.3A$13.ABC23.BA.B$39.A.C
#L $6.A4.A6.A$5.15A$6.A..A..A..A..A9$15.C$14.A.B$13.4A$12.A.A$12.B.A$12.C
#L 3A$14.A$14.A.C$4.ABC6.3AB$..A..A8.A.A$.6A5.A.A$..A3.AA4.B3A$..A4.AA3.C
#L .A24.CBA$.AA5.3A3.A25.A$A.A5.A.B..3AC22.3A$B.A5.A.C3.A.B21.BAA.A$C9A4.
#L A.A23.CB$..A..A..A3.4A$4.ABC5.B.A$11.AAC$11.AB$6.A4.A6.A$5.15A$6.A..A
#L ..A..A..A