James Propp<jpropp@cs.uml.edu> wrote:
If Conway were still posting to math-fun, he'd probably reply that I'd be better off just making numbered counters and moving them around. His early work on the Game of Life was done by hand, and he's of the opinion that some of the insights he gained from this couldn't have been gained if he'd just had a computer do the simulations.
Most of my early discoveries in Life were also done by moving counters around on a board. And once personal computers became readily available, most of my subsequent ones have been done by single-stepping patterns to observe the state transitions of single cells (rather than just running things at high speed for hundreds or thousands of generations). Sometimes, it can be useful to try to smash a glider into a pattern in every possible orientation (which is amenable to massive parallelization and iteration techiques), but much more often, problems require great precision. For example, synthesis of an object from gliders often requires a specific cell to be turned on or off at a specific time. This requires careful analysis of the entire history of specific cell and its immediate environment, and often requires complicated Rube-Goldberg style machinations. This requires finesse rather than brute force. David Buckingham, who has probably done most of the work on synthesizing most small objects (both simple and complicated) from gliders, would likely express similar sentiments. Many of his syntheses require making slight adjustments to random mushes that occur dozens or even hundreds of generations after gliders collide - which necessarily require observing such interactions in detail one generation at a time, something easy to do when advancing patterns slowly by hand (using counters or a computer), but which would be totally missed when running patterns at high speed. -- Mark D. Niemiec <mniemiec@gmail.com>