worms worms family cellular devised model behaviour feeding patterns certain prehistoric worms model worm moves points triangular grid line segments representing food determined configuration eaten line segments adjacent point worm currently despite governed simple rules behaviour worms extremely complex ultimate fate variant unknown worms studied early 1970s conway described june presented november mathematical games column electronic arts game worms interactive implementation worms time worm turn way lacks rule stops lets user chooses direction sets rule worm history worms attempt simulate behaviour prehistoric worms creatures fed sediment ponds avoided paths travelled food scarce food occurred patches worm interest stay near previous trails different species worm different innate rules close travelled paths stay turn sharp turn created computer worm trails inspired conway develop simple set rules study worms regular conway original model worm grid produced different species worm behaviour considered worms triangular grid worms described presented november mathematical games column later reprinted differed approach cellular developed time focused cells relationships simple computer models abstract accurately describe behaviour real creatures demonstrate simple rules rise patterns resembling tracks rules worm starts point infinite triangular grid starts moving meet point travelled unit distance arrives new point worm decides based distribution traversed direction directions relative worm point view worm encountered exact distribution leave encounters distribution way available worm dies simulation ends discussion different types worm depending direction turn encountering new type intersection different varieties worm classified systematically assigning direction number listing choice time new type intersection encountered directions numbered follows direction indicates worm continues travel straight ahead direction indicates worm right turn similarly directions worm travel direction traversed worm rule decides travel direction time choice direction time choice available worm choice usually explicitly listed worm begins continues straight line forever trivial case usually stipulated worm turn encounters point furthermore avoid mirror image symmetrical worm turn right hand turn worm dies returns origin time edges available origin lethal worm possible combinations worm rules seen following argument worm encounters eaten segments eaten sharp turn gentle situation shown figure encounters eaten segment leave remaining worm return origin character eaten segments location eaten segments important distinct combinations eaten segments approach directions offer choice departure directions making different alternatives worm encounters eaten segments choose remaining ones regardless distribution eaten segments segment left worm different combinations rules mirror image die having choices leaving distinct species infinite straight line worm included species eventually die patterns exhibit infinite behaviour settle repeating pattern return origin strongly believed infinite remains rules exhibit complicated behaviour die adopt obviously infinite pattern ultimate fate unknown developed new methods solving hours computer time rules solved leaving worms rules solved determined leaving according worm active based simulate worms extraordinary speeds behaviour considerably complex related rectangular grid worm longest path segments possible different species worm produce path necessarily traverse order common path shortest seven point symbol example path shown animated figure total different paths produced species
Paterson's worms