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C00002 00002	life[f81,jmc]		A competitive form of the Life game
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life[f81,jmc]		A competitive form of the Life game

	For a long time I have been looking for a competitive game
that would involve programming and would reward complicated and
creative constructions.  The discussion of Corewar 
COREWA[S77,JMC] represents and attempt in that direction, but I
haven't yet found anyone interested in programming it.  A much
simpler competive game can be based on Life.

	The basic idea is to modify Conway's Life game to have three
states for each cell, one state is called "off" or blank, and the other
two "on" states are called "white" and "black".  Whether a state is
on or off propagates exactly as in Life.  When a state is on, whether
it is white or black is determined by the following two rules.

	1. As in Life an off cell is turned on when exactly three
of its neighbors are on.  Its color then becomes the color of the
majority of its neighbors.

	2. An on cell remains on if two or three of its neighbors are
on.  Our tentative rule is that a cell changes color if it and its
neigbors vote in the majority for a different color.  Thus a cell
with two or three neighbors all of  the opposite color would change
color.

	Each player has a home area and chooses the initial configuration
of this area.  Presumably he would only use his own color.  The Life automaton
then starts.  A player will win if his color comes to "dominate"
the plane.
If the other color is wiped out, clearly
that's a win.  We also want to consider it a win if one player
increases the number of cells with his color without bound while the
other player's number of cells remains finite.  The rules must be adjusted
to give a good game.

	This version may be too dull, since everything is determined
at the beginning.  Therefore, it may be desirable to allow the players
to affect the course of the game dynamically by modifying the states
of the cells in areas they "control".

	For example, at each life step, either player may modify up to ten cells
in his home area, except that he may not modify any cell within
two units of a cell occupied by the opposite color.
A player may give commands to any LISP program to make his moves
for him, and this will be the only effective way to play.

	The programs belonging to the two players and the referee
that carries out the Life algorithm are time-shared at a fixed
ratio - equal for the two players.

	The game might proceed in stages with intervention after
(say) 100 life steps or perhaps after (say) 3m steps.
At each stage, each player is allowed to modify the configuration
of the area he controls subject to some limitation.  For example,
we might say that a player controls squares that are half as far
from his nearest occupied cell than from the nearest opponent
occupied cell, and at most 20 cells may be modified at each stage.

	Needless to say, the setting up of initial configurations
and modifications to positions are done privately, and the players
see what their opponents have done only after they have committed
themselves.

	Because of the geometry of Life, it may be worthwhile to
experiment with the topology.  For example, the board may be cylindrical
so that gliders fired in an appropriate direction are guaranteed
to reach enemy territory.  A toroidal game may be even more exciting.

	Fred Abrahamson suggests that the battle be for first occupation
of a single designated square symmetrically located with respect
to the players.

Remarks:

	1. Notice that the cellular automaton whose states are just
"on" and "off" operates just as in Conway's game.  Thus two-color
life is a kind of anti-homomorph or covering of Conway's life.  This
suggests a more general study of homomorphisms of cellular automaton
systems.

	2. The rules for changing color can depend on a different
set of neighbors than the rules for on and off.

	3. There could be different colored off cells.

	4. I have assumed that apart from the configurations set up
by the players, the rest of the board was blank.  This need not be
true.  We could imagine that there is a third weak color used in
an initial configuration seen by both players before they set up
their areas.  The weak color cannot convert a cell of some other
color even when a majority.  New cells always become white or black
if either is adjacent and not tied in number.

	5. Let me emphasize again that the goal in designing the
game is to put a premium on the ability to invent powerful initial
configurations in the static game and to adapt rapidly in the
variants where the players can intervene.

Jan 6
	6. One way of asserting control is like an arcade game.  Namely
a player can translate his first few rows horizontally any fixed number
of cells.  If he has glider guns in these rows, the effect will resemble
"space invaders".
Notes:

All gliders but one become homogeneous in color but
 w
w
wbb

oscillates between 3 white and two black and the reverse.  The geometric
phase and the color phase are synchronous.  Of course, it isn't clear
that mixed gliders can be emitted by any kind of mixed glider gun.