Discussion

The rules of the Black&White Game are suggested on the basis of a study of the case with 4 initial white cells countered by 2 black cells It so happens that in each of these cases (22 in all, since there are exactly 22 connected 4-cell figures) there is a winning response from black.

The case of 5 initial white cells is still wide open but one can conjecture that black will have a good chance with a 3-cell response. Hence the suggestion that black in general should respond with n-2 cells on white's initial n-cell pattern.

Note that in both these cases one black cell will die in the next generation which surprisingly not prevents the happy outcome. This is probably as close one can get to the sacrifice moves sometimes used in chess.

A little bath observation.

Here is a black cell taking a bath in a white pond.
Here the bathing cell is seen thrown ashore, white and clean.

The underdog wins.

Here white seems to have a solid 6-4 lead. But the beehive and the block are unfortunately too close to be stable.
Some generations later the situation is reversed. Now black is in the lead and wins since the pattern has become stable!

Spaceships

The above patterns are called lightweight, middleweight and heavyweight spaceship respectively. They all move two cells to the right in 4 generations, replicating themselves after 4 generations. The Black&White games that result from the insertion of two black cells are all won by black in spite of the uneven initial condition. This highlights the interesting question of the importance of different initial cells for the final stable or cyclic pattern. Obviously, the two black cells above have a very strong 'genetic' impact. This question can be studied in the Rainbow Life Game where the influence of e.g. black cells is visible in the colour of the offspring cells, since these colours are calculated as the arithmetic mean (in the RGB system) of the colours of the three parents.

The seagull.

This scene represents a baby seagull on its way out of the black egg. You may note the characteristic black wing tips already on this juvenile bird. The seagull then proceeds to the left and lays a white egg (some people would say a beehive) in the 21st generation.
After that it immediately turns around. The scene here shows the bird after its successful egg-laying on its way to the right. Note that the black wing tips are still there.

Then the seagull surprisingly lays a new white egg somewhat beyond the spot where it was born (in generation 36). It then turns around again and moves to the left towards its first egg, probably with the intent to lay still another egg. But the already existing egg disturbs the scene and everything ends in chaos and the black wing tips vanish. If however somebody removes the egg before the bird reaches the spot all works fine, a new egg is laid, the seagull turns around etc. So that, if you take away each seagull egg, the bird will continue indefinitely to produce one egg for every turn. It can be called a pseudo oscillator with period 30.
If these egg removing activities look like cheating, you may want to look at this honest version which is a genuine oscillator. The two blocks seem to function as aggressive cuckoo-eggs effectively killing the seagull's own eggs.

The seagull is also known as the 'queen bee' in its monochrome version, probably because of its tendency to fly between beehives. For details, see the 'queen bee shuttle' in the Conway's Life Glossary.(Alan Hensel).

Two queen bees can also be used as a 'glider gun', i.e. a pattern that regularly ejects gliders. See the item 'gun 30' under 'open' in Hensel's fast Life Game. or the Gosper gun in Eric W. Weisstein's compilation of Life forms. Such interesting constructions are examples of patterns that develop unboundedly many cells.

Black&White Game, further discussions.