introduction
instructions
tor5.lif
tor5.asm
tor5.com
tor5.dat
resume
:Introduction.

	TOR5.LIF is a protocol for executing life on a 5x5 torus.  If we
think of a grid

			 1  2  3  4  5
			 6  7  8  9 10
			11 12 13 14 15
			16 17 18 19 20
			21 22 23 24 25

it may be folded up into a torus by connecting the top edge to the bottom
edge, and the left margin to the right margin. This done, every cell has the
full set of eight neighbors which it needs for LIFE. Space is quite limited,
so every pattern will be quite crowded if it tries to expand. Since there are
only (!)only 2**25 (> 20,000,000) initial configurations possible, it is just
barely possible to analyze them all with some tens of hours of running time.

	Torus LIFE has applications to regular LIFE, because a torus is
just the same as an infinitely repeating periodic pattern whose basic cell
is the one sketched above. To study all of the LIFE patterns on a 5x5 torus
is the same as studying all the patterns with period 5 in each direction.
-
	This idea can be grasped a little more clearly if we repeat the
basic pattern three times vertically and horizontally:

		 1  2  3  4  5  1  2  3  4  5  1  2  3  4  5
		 6  7  8  9 10  6  7  8  9 10  6  7  8  9 10
		11 12 13 14 15 11 12 13 14 15 11 12 13 14 15
		16 17 18 19 20 16 17 18 19 20 16 17 18 19 20
		21 22 23 24 25 21 22 23 24 25 21 22 23 24 25
		 1  2  3  4  5  1  2  3  4  5  1  2  3  4  5
		 6  7  8  9 10  6  7  8  9 10  6  7  8  9 10
		11 12 13 14 15 11 12 13 14 15 11 12 13 14 15
		16 17 18 19 20 16 17 18 19 20 16 17 18 19 20
		21 22 23 24 25 21 22 23 24 25 21 22 23 24 25
		 1  2  3  4  5  1  2  3  4  5  1  2  3  4  5
		 6  7  8  9 10  6  7  8  9 10  6  7  8  9 10
		11 12 13 14 15 11 12 13 14 15 11 12 13 14 15
		16 17 18 19 20 16 17 18 19 20 16 17 18 19 20
		21 22 23 24 25 21 22 23 24 25 21 22 23 24 25

	Of course, to get regular LIFE it would have to be repeated
indefinitely often in all directions.

-
:Instructions.

	If you execute the program TOR5.COM,, there will be long stretches
of time during which it does not produce any output, and it will require about
forty hours of running time altogether (5MHz Intel 8085).

	Since its results are also placed in a file TOR5.DAT, you must execute
HJELP (TORU) using a disk which is not write-protected, and which has at least
10K space free. Because of its size and long running time, its execution is not
provided for in this HELP file.

	The following options are available:


		=   to see which state is executing
		S   to close TOR5.DAT and save memory in RTOR5.DAT
		^C  to close TOR5.DAT and exit from TOR5.COM





-

	The option = can be used to check progress when the program is not
producing any output.


	 If S is used, you can restart the program (but not from HJELP) by
executing RTOR5.COM. Before doing so it is advisable to rename TOR5.DAT if
you wish to keep the data already accumulated.


	Because it is somewhat too large to fit into Hjelp's present buffer,
TOR5.COM cannot be executed from HJELP.

:: (TORU)TOR5.LQF
: (TORU)TOR5.AQM  -  is too big for HJELP's buffer
: (TORU)TOR5.COM  -  is to big for HJELP's buffer
:: (TORU)TOR5.DQT
:Resume.

	On the 5x5 torus there are

		 1  zero field
		32  still lifes
		13  period 2 cycles
		 1  3-cycle
		 3  4-cycles
		 1  5-cycle
		 0  6-cycles
		 0  7-cycles
		 0  8-cycles
		 0  9-cycles
		>3 10-cycles
		>1 20-cycles

	All these figures count all the symmetric images of a configuration
as one single item.

:[end]
[Harold V. McIntosh, 5 August 1985]
