- author = "Michael D. Schmidt and Hod Lipson",
- title = "Solving iterated functions using genetic programming",
- booktitle = "GECCO-2009 Late-Breaking Papers",
- year = "2009",
- editor = "Anna I. Esparcia and Ying-ping Chen and Gabriela Ochoa and Ender Ozcan and Marc Schoenauer and Anne Auger and Hans-Georg Beyer and Nikolaus Hansen and Steffen Finck and Raymond Ros and Darrell Whitley and Garnett Wilson and Simon Harding and W. B. Langdon and Man Leung Wong and Laurence D. Merkle and Frank W. Moore and Sevan G. Ficici and William Rand and Rick Riolo and Nawwaf Kharma and William R. Buckley and Julian Miller and Kenneth Stanley and Jaume Bacardit and Will Browne and Jan Drugowitsch and Nicola Beume and Mike Preuss and Stephen L. Smith and Stefano Cagnoni and Jim DeLeo and Alexandru Floares and Aaron Baughman and Steven Gustafson and Maarten Keijzer and Arthur Kordon and Clare Bates Congdon and Laurence D. Merkle and Frank W. Moore",
- pages = "2149--2154",
- address = "Montreal",
- publisher = "ACM",
- publisher_address = "New York, NY, USA",
- month = "8-12 " # jul,
- organisation = "SigEvo",
- keywords = "genetic algorithms, genetic programming",
- isbn13 = "978-1-60558-325-9",
- bibsource = "DBLP, http://dblp.uni-trier.de",
-
DOI = "
doi:10.1145/1570256.1570292",
- size = "5 pages",
- abstract = "An iterated function f(x) is a function that when composed with itself, produces a given expression f(f(x))=g(x). Iterated functions are essential constructs in fractal theory and dynamical systems, but few analysis techniques exist for solving them analytically. Here we propose using genetic programming to find analytical solutions to iterated functions of arbitrary form. We demonstrate this technique on the notoriously hard iterated function problem of finding f(x) such that f(f(x))=x2--2. While some analytical techniques have been developed to find a specific solution to problems of this form, we show that it can be readily solved using genetic programming without recourse to deep mathematical insight. We find a previously unknown solution to this problem, suggesting that genetic programming may be an essential tool for finding solutions to arbitrary iterated functions.",
-
notes = "Bronze 2010 HUMIES GECCO 2010
Distributed on CD-ROM at GECCO-2009.
ACM Order Number 910092.",
