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Echoes and traces are two common uses of the odd bitplanes, although echoes may be made to any of the other bitplanes. Indeed, Zhabotinsky type rules incorporate the echo into counters and thence into the rule of evolution itself.

Simple echoes have artistic value, and are even useful as indicators of the ages of cells. Cumulative echoes are often employed in automata such as Life , to give an indication of how far an initial configuration expanded before it stabilized or died out.

But Life is also a good example of an automaton in which a trace may be used to advantage. As is well known, gliders have a special significance in Life , so one might ask about where the gliders are. Fortunately, a glider fits quite snugly into a single Moore neighborhood; a good rule for the odd plane accompanying a Life plane would be to accumulate those cells whose neighborhoods ever contained a glider. Gliders have two phases, move in four directions, and have mirror images; the rule can detect any or all of them.

The result of such a composite rule looks somewhat like a nuclear emulsion. Many neighborhoods will contain gliders, surrounded by live cells which interfere with the glider; there ought to be quite a few marked cells. Indeed, rough estimates of how many of the neighborhoods would be shaped like a glider show that they are not at all uncommon, perhaps comprising 3% of all neighborhoods. But whenever a glider breaks loose or travels freely, it will leave a diagonal line behind; those are the tracks to be counted.

Harold V. McIntosh