How to use this applet: Start the game by drawing a pattern on the game board using the mouse, then click start. You may change the life rules by clicking the ecology button. The rule changes will take effect as soon as you click apply even if the game is running. However, if you select a classic pattern from the choice box the pattern will not be applied unless the game is stopped, and the previous game board will be erased. The "reset to defaults" button in the ecology dialog will reset the game rules to Conway's original rules. These rules are: with each step a cell counts the number of its neighbors. If there are exactly 3 neighbors, then if the cell is dead, it comes to life. If it is currently alive, then if there are exactly 2 or 3 neighbors it will survive, otherwise it will die.
The Game of Life is like a simple brain
The Game of Life was invented by the mathemetician John Conway in 1970 and became popular as a simple example of "artificial life". Conway's rules for the game produce patterns that move and resemble crawling creatures. It was one of the first computer games, and computing Life patterns used an enormous number of after-work-hours CPU time on 1970's minicomputers. But to me the game resembles "life" less than it resembles a simple "brain". Think of the board squares as nerve cells that detect the state of their nearest neighbors. They are never "dead", only "active" or "inactive", depending on whether their neighbors are active. The game board shown here is 50 x 50, so it would be a "brain" with 2500 neurons.
If the game board with its cells is like a simple brain, then when a cell is "on" it is like a neuron that is "firing", and the patterns shown on the board are a kind of "behavior pattern". Let's regard the patterns seen with Conway's rules as "normal" behavior, and experiment with changes in the rules to see how they can produce "abnormal" behavior.
The normal rules produce stable repeating patterns
These rules produce interesting little "creatures" that move around the board. Uncounted numbers of people have spent many hours describing new patterns seen with the normal rules. You can see some of the more interesting patterns by selecting them from the choice box in the ecology dialog. Some of them repeat only with long cycles--the glider moves all the way around the board before it repeats. Some of them seem not to repeat at all for a long time, such as the r-pentomino, but after 1103 generations even this settles into a stable or repeating pattern. Although computing stable repeating patterns may be a natural thing for computers to do, such stability and repetitiveness isn't good for living things, and certainly isn't good for something that should be flexible and creative, like a brain.
Conclusion: There is a "little life lesson" here--even good rules and a good starting pattern can lead to a stable, dull, uncreative state. This is a terrible fate.
How can we avoid stable repeating patterns?
One way is to put in a little randomness.
Do this experiment: Open the ecology dialog and start the game with an r-pentomino and Conway's rules (select r-pentomino from the choice box in the ecology dialog). Notice that after many generations the pattern becomes stable. Now do it again, but add some randomness. Ten parts in 100,000 (0.01%) randomness are sufficient to prevent complete stability. (The random level represents the chance in any one game step that any one dead cell will randomly come to life. Sorry about the buggy WIN32 Java scrollbar. When I get time I'll write a custom, non-buggy scrollbar.)
Do another experiment: Now add a lot of randomness, say 2000 (2%). Now there's so many cells randomly firing that you don't see the normal patterns much at all.
Insofar as the Game of Life resembles a brain, we may now conclude: "To avoid stable repeating behavior patterns you may introduce some randomness. But don't overdo it--very little will do the trick".
Discussion: The random numbers are generated by the Java runtime system. They are pseudorandom, not truly random, and the results might be different with really random numbers. In addition,the random numbers used for the program are selected from a uniform distribution, which may not be a "natural" kind of randomness. Interesting future experiments might be: test the effect of using truly random numbers (see www.random.org), or random numbers with specific distributions, say a Gaussian distribution.
Is there any way to avoid stable repeating patterns besides using randomness?
Yes. One way is to allow cells to survive even without neighbors.
Do this experiment: Use the normal rules and start with an r-pentomino pattern, but allow single cells with no neighbors to survive (survive on 0,2,3). The effect is to leave little single spots on the board that can serve as a way to disrupt stable patterns. Using these rules, the game can go on a very long time without ever becoming stable or repeating. But note that this disrupts the normal patterns--the board is messy.
Conclusion: Just changing the rules won't do--sometimes you just need a few randomly firing cells to break out of your rut. And allowing all the little bitty ideas to occupy your thoughts just makes the whole pattern messy.
There is at least one more way to break out of a stable repeating pattern, and it is the best way. I call it the "therapy way"
Do this experiment: Start the game with an r-pentomino and Conway's rules. Let it run until there is a stable repeating pattern. It will include several rotating crosses. Now do "therapy"--select one of the crosses, and use the mouse to click on the end of it (be sure that the mouse is "creating" rather than "destroying". If nothing happens, try it again. If all goes well, the cross will change into a small oval. Click again on the end of the oval. If your "therapy" is good, the area you clicked on will enlarge to involve a large part of the game board. A good "therapist" can pick just one or two spots to click on to get the whole thing started going again. Of course, the pattern will eventually settle down again into a stable repeating one, and you will have to do therapy again. Nevertheless, this method requires many fewer game board changes than does adding randomness or allowing zero-neighbor cells to survive.
Conclusion: Therapy may be the best way to avoid mental gridlock, if you can get a good therapist.
This particular example of "therapy" isn't too hard, but other patterns are more difficult to break out of
Do this experiment: Start the game with a fish pattern. The fish will swim across the game board over and over again. It is a stable pattern that repeats with a long cycle. Try using the mouse to break it out of this pattern. The first few times, you're more likely to destroy the fish than to break it out of its stable pattern. (Hint: try clicking in the fish tail rather than in its head.)
Conclusion: Some behavior patterns are more difficult to break out of than others.
The behavior of the system is very dependent on the exact rules
Do this experiment: Start with an r-pentomino pattern and normal rules, and let it run for awhile. While it is running, open the ecology dialog and change the rules to allow cells with four neighbors to survive. Notice how the game board quickly becomes filled up with lines having little movement--a stiff, inflexible, crowded pattern. It doesn't look very much like either a normal behavior pattern or an interesting Game of Life. It isn't even very pretty. Try correcting the pattern by destroying a few cells (click on destroy and then drag the mouse through the game board). Even this drastic therapy doesn't help much--some cells may quiver for awhile, but it doesn't last long, because the rules mandate that the board look just this way. For this pathological behavior to be corrected, the rules must be changed. Try clicking off survival on four, then apply the new rule--the pattern quickly dissolves into a more normal one.
Conclusion: Some rules cause especially pathological behavior, but recovery is possible if the bad rule is changed.
Some rule changes have little effect
Experiment: Start with an r-pentomino and normal rules, but allow cells with eight neighbors to survive. Notice the stable repeating pattern that results. Compare it to the pattern that results if survival with eight neighbors is not allowed. They are different, but only subtly so. It seems that cells have eight neighbors so little of the time that the rule has little effect.
Conclusion: Some rules aren't bad, they're just different.
Altering birth rules produces paroxysmal behavior--like a seizure
In people or animals, a seizure is a sudden change in behavior thought to be due to sudden paroxymal firing of brain cells. The Game of Life can also have paroxysmal behavior.
Do this experiment: The simplest way to produce paroxysms--sudden generalized changes from one pattern to another--is to set birth =0 and survival to none. The board will flip back and forth from completely off to completely on at each step. If you draw figures into the board, they also flip back and forth.
Do another experiment: A similar rules change will disrupt an ongoing normal pattern. Start with an r-pentomino and normal rules and let it run awhile. Then set birth =0. The board again begins its paroxysmal flashing, which slowly--not immediately--disrupts the normal pattern contained within the flashing.
Do another experiment: Allow birth with just one neighbor, or 2, 4, or 5. Different patterns are produced, but all completely disrupt the normal pattern. Allowing birth with 6 or more is less dramatic--the pattern is disrupted, but slowly, and the new pattern grows slowly. The effects of birth on 7 or 8 are quite subtle, and not very paroxysmal at all.
Conclusion: Certain rules in the Game of Life produce seizure-like patterns.
Altering survival rules produces abnormal, but not paroxysmal, behavior
Do this experiment: Use the default rules, but also allow survival with 0,1,4,5,6,7,or 8 neighbors. Survival with zero neighbors allows the board to get spotted with single cells, as we saw earlier. Survival with 1 disrupts the development of the r-pentomino. Survival with 4 causes the board to get filled with lines that don't allow any movement. Survival with 5 or 6 don't abolish movement, but the pattern is one with large wiggly areas rather than small moving "creatures". Survival with 7 or 8 neighbors also changes the pattern, but subtly so. The changes are most apparent if you watch highly structured patterns that are supposed to change in a precise way. Survival with 7 neighbors disrupts the "gun" classic pattern for example. Survival with 8 disrupts growth of the "row of 10" pattern so that it dies out, but once it's settled into a stable repeating pattern, adding survival on 8 doesn't hurt it.
Conclusion: Certain rules changes don't cause anything real dramatic--they just make it hard to grow or difficult to "think".
What about deleting the normal rules?
Do this experiment: What about subtracting from the normal rules? Try it--deleting the survive on 3 rule has amazingly little effect, but deleting the survive on 2 or the birth on 3 rules are quickly lethal to most patterns.
Conclusion: Conway's rules are just about the minimum necessary to sustain "life" or "thought".
And then there's complete craziness...it may be beautiful
The patterns we have examined so far are mainly produced by additions to the Conway's normal rules. What happens if we just dispense with Conway's rules altogether and study some completely different ones? Try it and see.
Do this experiment: One of my favorite rules produces "snowflakes" with 4 part rather than 6-part symmetry. "Snowflake rules" are: birth on only 1 neighbor, no survival. Erase the screen, then click once in the middle to start the snowflakes. This produces a simple blocky pattern. Produce subtle variations in snowflake patterns by liberalizing the birth or survival rules. I especially like birth = 1, 2, 3 with survive = 2, 3.
Conclusion: It may be crazy, but it's pretty.
How much like a brain is the Game of Life?
Not much in one sense, because it doesn't seem to be able to do anything useful. But let's not hold that against it, because if all we could see is the firing patterns of our own brain cells, they wouldn't appear to be doing anything useful either. In a broad sense, these are the ways the Game of Life resembles a brain:
- Its activity is highly patterned.
- When it's operating normally, the precise patterns are not predictable.
- Random firing occurs in the brain. In the Game of Life random firing prevents excessive stability.
- Under certain conditions, paroxysmal patterns occur in both the brain and in the Game of Life.
- In the Game of Life, as in the brain, the "program" and the "data" are the same thing.
Can the Game of Life be modified to make it even more like a brain? Maybe so. Next we'll explore a cellular automaton like the Game of Life called "Brian's Brain". Stay tuned.