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According to the already established nomenclature in the literature, we present the relevant phenomenology organized in different scenarios: fractal islands disaggregation, finite disaggregation, infinitely disconnected basin, infinitely many converging sequences of lakes, countable self-similar disaggregation and sharp fractal boundary. By use of critical curves, we determine the influence of zones with different number of first rank preimages in the mechanisms of basin fractalization. <\/jats:p>","DOI":"10.1142\/s0218127403006558","type":"journal-article","created":{"date-parts":[[2003,3,18]],"date-time":"2003-03-18T16:24:52Z","timestamp":1048004692000},"page":"287-310","source":"Crossref","is-referenced-by-count":12,"title":["COMPLEX PATTERNS ON THE PLANE: DIFFERENT TYPES OF BASIN FRACTALIZATION IN A TWO-DIMENSIONAL MAPPING"],"prefix":"10.1142","volume":"13","author":[{"given":"RICARDO","family":"L\u00d3PEZ-RUIZ","sequence":"first","affiliation":[{"name":"Facultad de Ciencias \u2013 Edificio B, \u00c1rea de Ciencias de la Computaci\u00f3n, Universidad de Zaragoza, 50009 \u2013 Zaragoza, Spain"}]},{"given":"DANI\u00c8LE","family":"FOURNIER-PRUNARET","sequence":"additional","affiliation":[{"name":"Institut National des Sciences Appliqu\u00e9es, Syst\u00e8mes Dynamiques (SYD), L.E.S.I.A., Avenue de Rangueil, 31077 Toulouse Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1936-1"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000458"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000446"},{"key":"rf4","volume-title":"Iterated Maps on the Interval as Dynamical Systems","author":"Collet P.","year":"1980"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/9789814415712_0008"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000506"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497000972"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127494000125"},{"key":"rf9","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0089135","volume-title":"Recurrences and Discrete Dynamical Systems","author":"Gumowski I.","year":"1980"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.29.275"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.31.3868"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0960-0779(91)90041-7"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000410"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90001-6"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.5991"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1142\/0413"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127494000241"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127495000752"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/2252"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3486-9"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.279"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.35.3115"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.31.3332"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.28.1662"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403006558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:07:27Z","timestamp":1565190447000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403006558"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":24,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,2]]}},"alternative-id":["10.1142\/S0218127403006558"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403006558","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}