{"abstracts":[{"sha1":"72df83ba559a04c15f5ded8361d91d8efbd5ec86","content":"This article introduces new tools to study self-organisation in a family of\nsimple cellular automata which contain some particle-like objects with good\ncollision properties (coalescence) in their time evolution. We draw an initial\nconfiguration at random according to some initial σ-ergodic measure\nμ, and use the limit measure to descrbe the asymptotic behaviour of the\nautomata. We first take a qualitative approach, i.e. we obtain information on\nthe limit measure(s). We prove that only particles moving in one particular\ndirection can persist asymptotically. This provides some previously unknown\ninformation on the limit measures of various deterministic and probabilistic\ncellular automata: 3 and 4-cyclic cellular automata (introduced in [Fis90b]),\none-sided captive cellular automata (introduced in [The04]), N. Fatès'\ncandidate to solve the density classification problem [Fat13], self\nstabilization process toward a discrete line [RR15]... In a second time we\nrestrict our study to to a subclass, the gliders cellular automata. For this\nclass we show quantitative results, consisting in the asymptotic law of some\nparameters: the entry times (generalising [KFD11]), the density of particles\nand the rate of convergence to the limit measure.","mimetype":"text/plain","lang":"en"},{"sha1":"844723b3de76782c620d2350ef59693bb3424d35","content":"This article introduces new tools to study self-organisation in a family of\nsimple cellular automata which contain some particle-like objects with good\ncollision properties (coalescence) in their time evolution. We draw an initial\nconfiguration at random according to some initial $\\sigma$-ergodic measure\n$\\mu$, and use the limit measure to descrbe the asymptotic behaviour of the\nautomata. We first take a qualitative approach, i.e. we obtain information on\nthe limit measure(s). We prove that only particles moving in one particular\ndirection can persist asymptotically. This provides some previously unknown\ninformation on the limit measures of various deterministic and probabilistic\ncellular automata: 3 and 4-cyclic cellular automata (introduced in [Fis90b]),\none-sided captive cellular automata (introduced in [The04]), N. Fat{\\`e}s'\ncandidate to solve the density classification problem [Fat13], self\nstabilization process toward a discrete line [RR15]... In a second time we\nrestrict our study to to a subclass, the gliders cellular automata. For this\nclass we show quantitative results, consisting in the asymptotic law of some\nparameters: the entry times (generalising [KFD11]), the density of particles\nand the rate of convergence to the limit measure.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Benjamin Hellouin de Menibus","role":"author"},{"index":1,"raw_name":"Mathieu Sablik","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v1","ext_ids":{"arxiv":"1602.06093v1"},"release_year":2016,"release_date":"2016-02-19","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["hnw2zlfr7ngznpkcqxiwohowuu"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/1602.06093v1.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20200911093730/https://arxiv.org/pdf/1602.06093v1.pdf","rel":"webarchive"}],"sha256":"36be8285dd35e94cf6453315c729fb545befc1b8d487ccd08febdb83c2a78444","sha1":"14e5231e437b1d234fab65885cc62a16f2672881","md5":"293cf4bf68431e51a5beba5e2c3d3c5c","size":1043708,"revision":"182a25fe-03f7-4d07-8333-e0555d1edfe5","ident":"7mmdvoy6ljbxlhmda7xg53nwzm","state":"active"}],"work_id":"bilsxydtbjch7fjbqygr6fh5lq","title":"Self-organisation in cellular automata with coalescent particles:\n qualitative and quantitative approaches","state":"active","ident":"hnw2zlfr7ngznpkcqxiwohowuu","revision":"876cf461-73e3-48c0-aa1b-cc685cb45682","extra":{"arxiv":{"base_id":"1602.06093","categories":["math.DS","cs.MA","math.PR"],"journal_ref":"Journal of Statistical Physics, Springer Verlag, 2017, 167 (5),\n pp.1180 - 1220"},"superceded":true}}