{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T16:41:20Z","timestamp":1769877680139,"version":"3.49.0"},"reference-count":44,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,12,15]]},"abstract":"<jats:p>This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton\u2019s laws of motion to the astronomy of Poincar\u00e9 and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA\u2019s discovery and use of zero-fuel chaotic \u201csuperhighways\u201d between the planets; erratic chaotic solutions generated by Euler\u2019s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.<\/jats:p>","DOI":"10.1142\/s0218127416300354","type":"journal-article","created":{"date-parts":[[2016,12,29]],"date-time":"2016-12-29T09:22:06Z","timestamp":1483003326000},"page":"1630035","source":"Crossref","is-referenced-by-count":18,"title":["Chaos, Fractals and Their Applications"],"prefix":"10.1142","volume":"26","author":[{"given":"J. Michael T.","family":"Thompson","sequence":"first","affiliation":[{"name":"Department of Applied Maths and Theoretical Physics, University of Cambridge, CB3 0WA, UK"}]}],"member":"219","published-online":{"date-parts":[[2016,12,29]]},"reference":[{"key":"S0218127416300354BIB001","volume-title":"An Introduction to Dynamical Systems","author":"Arrowsmith D. K.","year":"1990"},{"key":"S0218127416300354BIB002","volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"Bernardo M.","year":"2008"},{"key":"S0218127416300354BIB004","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1286-46"},{"key":"S0218127416300354BIB005","doi-asserted-by":"publisher","DOI":"10.5962\/bhl.title.59991"},{"key":"S0218127416300354BIB006","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195096705.001.0001","volume-title":"An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns","author":"Epstein I. R.","year":"1998"},{"key":"S0218127416300354BIB007","volume-title":"Fractal Geometry","author":"Falconer K.","year":"1990"},{"key":"S0218127416300354BIB009","doi-asserted-by":"publisher","DOI":"10.1126\/science.1519060"},{"key":"S0218127416300354BIB010","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0290-42"},{"key":"S0218127416300354BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608556"},{"key":"S0218127416300354BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-460X(82)80002-3"},{"key":"S0218127416300354BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511616051"},{"key":"S0218127416300354BIB015","doi-asserted-by":"publisher","DOI":"10.1063\/1.166509"},{"key":"S0218127416300354BIB016","volume-title":"The Variational Principles of Mechanics","author":"Lanczos C.","year":"1962","edition":"2"},{"key":"S0218127416300354BIB017","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2012.0423"},{"key":"S0218127416300354BIB019","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"S0218127416300354BIB021","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1994.0101"},{"key":"S0218127416300354BIB022","volume-title":"An Essay on the Principle of Population","author":"Malthus T.","year":"1798"},{"key":"S0218127416300354BIB023","doi-asserted-by":"publisher","DOI":"10.1119\/1.13295"},{"key":"S0218127416300354BIB024","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"S0218127416300354BIB025","doi-asserted-by":"publisher","DOI":"10.1002\/9783527617500"},{"key":"S0218127416300354BIB026","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0388-80"},{"key":"S0218127416300354BIB027","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"S0218127416300354BIB028","volume-title":"Fractals for the Classroom. Part 1: Introduction to Fractals and Chaos","author":"Peitgen H.-O.","year":"1992"},{"key":"S0218127416300354BIB029","volume-title":"Newton\u2019s Clock: Chaos in the Solar System","author":"Peterson I.","year":"1993"},{"key":"S0218127416300354BIB030","volume-title":"Les Methodes Nouvelles de la M\u00e9canique Celeste","volume":"1","author":"Poincar\u00e9 H.","year":"1899"},{"key":"S0218127416300354BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0771-5"},{"key":"S0218127416300354BIB033","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(76)90101-8"},{"key":"S0218127416300354BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(83)90115-X"},{"key":"S0218127416300354BIB035","volume-title":"The Dripping Faucet as a Model Chaotic System","author":"Shaw R.","year":"1984"},{"key":"S0218127416300354BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.piutam.2016.03.005"},{"key":"S0218127416300354BIB037","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2011.0161"},{"key":"S0218127416300354BIB038","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11798-1"},{"key":"S0218127416300354BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(89)90699-8"},{"key":"S0218127416300354BIB040","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/3527602585.ch7","volume-title":"Nonlinear Dynamics of Production Systems","author":"St\u00e9p\u00e1n G.","year":"2004"},{"key":"S0218127416300354BIB041","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(83)90111-2"},{"key":"S0218127416300354BIB042","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(82)90248-1"},{"key":"S0218127416300354BIB044","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1989.0009"},{"key":"S0218127416300354BIB045","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1990.0022"},{"key":"S0218127416300354BIB047","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1952.0012"},{"key":"S0218127416300354BIB048","volume-title":"The Road to Chaos","author":"Ueda Y.","year":"1992"},{"key":"S0218127416300354BIB049","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740200511X"},{"key":"S0218127416300354BIB051","doi-asserted-by":"publisher","DOI":"10.1142\/3345"},{"key":"S0218127416300354BIB052","doi-asserted-by":"publisher","DOI":"10.1016\/0019-1035(84)90032-0"},{"key":"S0218127416300354BIB053","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-6020-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416300354","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T13:41:12Z","timestamp":1718977272000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416300354"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,15]]},"references-count":44,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2016,12,29]]},"published-print":{"date-parts":[[2016,12,15]]}},"alternative-id":["10.1142\/S0218127416300354"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416300354","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,15]]}}}