{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T11:30:55Z","timestamp":1649071855153},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[1996,10]]},"abstract":"<jats:p> Wolfram\u2019s cellular automata [1986] can be classified according to their asymptotic behavior: class I (homogeneous), class II (periodic), class III (chaotic) and class IV (\u201cundecidable\u201d, i.e. erratically changing between periodicity and chaos). While these automata are purely number-theoretical and suffer from ill-defined parametrization, we present here examples of automata describing actual physical systems and governed by well-defined control parameters: resting states between earthquakes, pigmentation on the shells of molluscs, and two-dimensional reaction\u2013diffusion systems. We find that the dynamics of these three systems can be classified analogously to Wolfram\u2019s automata. Moreover, we find agreement between class IV simulations and real shell patterns, indicating that these shells indeed present evidence for class IV behavior in nature. In addition, we performed an intuitively appealing quantification by averaging the fluctuations of the borders of error-propagation patterns. <\/jats:p>","DOI":"10.1142\/s0218127496001156","type":"journal-article","created":{"date-parts":[[2004,10,6]],"date-time":"2004-10-06T11:19:50Z","timestamp":1097061590000},"page":"1817-1827","source":"Crossref","is-referenced-by-count":5,"title":["CLASS IV BEHAVIOR IN CELLULAR AUTOMATA MODELS OF PHYSICAL SYSTEMS"],"prefix":"10.1142","volume":"06","author":[{"given":"MARIO","family":"MARKUS","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Molekulare Physiologie, Postfach 10 26 64, D-44026 Dortmund, Germany"}]},{"given":"INGO","family":"KUSCH","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Molekulare Physiologie, Postfach 10 26 64, D-44026 Dortmund, Germany"}]},{"given":"ANT\u00d3NIO","family":"RIBEIRO","sequence":"additional","affiliation":[{"name":"Departamento de Geologia, Faculdade de Ci\u00eancias, Universidade de Lisboa, 58, rua da Escola Polit\u00e9cnica, P-1200 Lisboa, Portugal"}]},{"given":"PEDRO","family":"ALMEIDA","sequence":"additional","affiliation":[{"name":"Departamento de Geologia, Faculdade de Ci\u00eancias, Universidade de Lisboa, 58, rua da Escola Polit\u00e9cnica, P-1200 Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127496001156","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:17:34Z","timestamp":1565129854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127496001156"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,10]]},"references-count":0,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1996,10]]}},"alternative-id":["10.1142\/S0218127496001156"],"URL":"https:\/\/doi.org\/10.1142\/s0218127496001156","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,10]]}}}