Lyapunov Exponents

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One of the most fascinating offshoots from chaos theory involves the generation and analysis of equations using Lyapunov exponents. For our purposes, the eye appeal of graphics plots of so-called Lyapunov Space takes center focus.

  Lyapunov Space     The Swallow           Jellyfish              Zircon Zity    
lyap1.jpg (41887 bytes)    swallow.jpg (67647 bytes)    jfish.jpg (46432 bytes)    zzity.jpg (74580 bytes)

The names of these images were taken from the original article in Scientific American. (See "Leaping into Lyapunov Space", by A. K. Dewdney, Scientific American, Sept. 1991, pp. 178-180.) 

The thumbnails above are linked to the full images they represent. Each of the full images was generated by an application you can download here. This executable is a very high performance Lyapunov image creator which is able to complete an image in less than 20 seconds on a 500MHz Pentium.