I discovered the glider by hand. Mike Guy & I wrote the first computer programme, but it ran so fast as to be useless, and all the early discoveries were made pushing counters around. R.
Coincidentally, there recently transpired on the Life mailing list rwg>Subj:Earliest (middle)weight spaceship ((M)WSS) gun I showed two young brothers Golly and the p(eriod)30 gun, and they went to town crossing beams and quickly found the "Five and Dime" p150 and 300 pulse divider, etc. But I'm not sure they noticed the configuration where the 7th glider makes a MWSS and the 8th glider kills it. (Blame speed if they didn't.) So, long before the 3-glider *WSS syntheses, we got a MWSS gun by killing that 8th glider. And the 9th and 10th, since the only p240 would have been tripled period doublers. [We hadn't yet thought to thin streams with shuttling gliders, as below] But I'd forgotten that you also need some sort of cleanup at the collision point. It may have been as gross as another p300. Just now, I tried a couple of eaters, which hurried the MWSS birth from the 7th glider to the 5th, enabling p180 MWs. But unused gliders kill one of the eaters, necessitating another gun: x = 253, y = 159, rule = B3/S23 87b2o$79bo7bo2bo$78bo3b2o7bo9bobo$78bo5bo6bo7bo3bo$79b5o7bo7bo12b2o$ 87bo2bo7bo4bo8b2o$87b2o10bo$99bo3bo$90bobo8bobo$90b2o$91bo5$84bo$82b2o $83b2o6$75bobo$75b2o$76bo5$69bobobo$67b2ob2o2bo$68b3obo76bo$149b3o$ 152bo$151b2o8b2o$161bo$159bobo$109b3o47b2o$109bo$110bo43$94b3o$94bo$ 95bo3$200b2o$104b2o93b2o$105b2o94bo$104bo4$208bo$97bo109b2o$97b2o108bo bo$96bobo3$2o$o$bo213b2o$2o24bo62b2o123b2o$24bobo63b2o124bo$25b2o62bo 2$136bo$133b4o$124bo7b4o9b2o76bo$82bo40bobo6bo2bo9b2o75b2o$82b2o27b2o 9bo3b2o4b4o5bo52bo27bobo$81bobo27b2o9bo3b2o5b4o4bo51bo$122bo3b2o8bo56b 3o$123bobo$124bo$133bobo$134b2o94b2o$74b2o58bo94b2o10bobo$75b2o154bo8b o2bo4bo$74bo151b2o11b2o5b2o$226bobo8b2o3bo8b2o$221b2o6bo9b2o10b2o$141b o75b2obo2bo2bo2bo10bo2bo$142b2o73b2o2b2o6bo11bobo$67bo73b2o83bobo$67b 2o80bo76b2o$66bobo79bo$150bo$148b2o$149b2o$148bobo$149b2o$59b2o88bo$ 60b2o$59bo5$52bo$52b2o$51bobo6$44b2o$32bobo10b2o$27bo4bo2bo8bo$28b2o5b 2o11b2o121bob2o$23b2o8bo3b2o8bobo121b2obo$23b2o10b2o9bo6b2o$32bo2bo10b o2bo2bo2bob2o$32bobo11bo6b2o2b2o$47bobo$48b2o! Does anyone remember how the p300 worked? Gardner mentioned it in his column but it must have been too clunky to illustrate. Especially since his editors were pressuring him to drop Life because it was only interesting to the computered elite. --rwg
Brice Due> ... I recall getting out a ruler & pen and marking off
a grid on a piece of cardboard. Armed with 2 or 3 different colors of hole-puncher'd dots I performed a two-pass-per-gen raster algorithm by hand and got your glider gun to emit several gliders before the board got "bumped" one day.
Apple ][+ low-res in 6502 assembler happened later...
-brice
On Fri, 24 Jul 2009, rwg@sdf.lonestar.org wrote:
James Propp<jpropp@cs.uml.edu> wrote:
If Conway were still posting to math-fun, he'd probably reply that I'd be better off just making numbered counters and moving them around. His early work on the Game of Life was done by hand, and he's of the opinion that some of the insights he gained from this couldn't have been gained if he'd just had a computer do the simulations.
Mark understates the incredible skill required to smash gliders together to synthesize a prescribed object. Single step all I want, it still looks like magic. Here's Buckingham's Barber Pole synthesis, which, if it were Mark's, would be a Polish Joke. Download a Life player, paste this in, and single step until you get the idea:
x = 162, y = 157, rule = S23/B3 bo$bbo$3o5$159bo$10bo148bobo$11boo146boo$10boo5$151bobo$21bo129boo$19b obo130bo$20boo4$144bo$143bo$29bobo111b3o$30boo$30bo4$137bo$40bo94boo$ 41bo94boo$39b3o5$128bo$49bo78bobo$50boo76boo$49boo5$120bobo$60bo59boo$ 58bobo60bo$59boo4$113bo$112bo$73bobo36b3o$74boo$74bo$$85bo$86bo$84b3o 6$80boo7bo$79bobo6boo$81bo6bobo10$71boo$72boo$71bo11$69b3o$60boo9bo$ 59bobo8bo38boo$61bo47bobo$64b3o42bo$66bo$65bo3$60bo$60boo$50boo7bobo$ 51boo64boo$50bo4bo60boo$55boo61bo$54bobo4$50boo$49bobo$40b3o8bo$42bo 81b3o$41bo3boo77bo$44bobo78bo$46bo4$40boo$31bo9boo$31boo7bo92bo$30bobo 99boo$35boo95bobo$36boo$35bo4$30b3o$21boo9bo$20bobo8bo108boo$22bo117bo bo$25b3o112bo$27bo$26bo3$21bo$21boo$11boo7bobo$12boo134boo$11bo4bo130b oo$16boo131bo$15bobo4$11boo$10bobo$b3o8bo$3bo151b3o$bbo3boo147bo$5bobo 148bo$7bo!
If you liked that, try x = 30, y = 35, rule = B3/S23 13bo$13bobo$13b2o2$6bo$4bobo$5b2o3$8bo14bobo$9bo13b2o$7b3o14bo5$18bo$ 17b2o$17bobo$8b2o$7bobo18bo$9bo17b2o$2o25bobo$b2o11b2o$o7b2o5b2o$9b2o 3bo$8bo2$19b2o$19bobo$19bo2$9b2o$8bobo$10bo! --rwg
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>
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun