Cobweb plot

An animated cobweb diagram of the logistic map $y=rx(1-x)$ , showing chaotic behaviour for most values of $r>3.57$ .

A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in dynamical systems, a field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map. The technique was introduced in the 1890s by E.-M. Lémeray.^[1] Using a cobweb plot, it is possible to infer the long-term status of an initial condition under repeated application of a map.^[2]

^ Lémeray, E.-M. (1897). "Sur la convergence des substitutions uniformes" (PDF). Nouvelles annales de mathématiques, 3e série. 16: 306–319.
^ Stoop, Ruedi; Steeb, Willi-Hans (2006). Berechenbares Chaos in dynamischen Systemen [Computable Chaos in dynamic systems] (in German). Birkhäuser Basel. p. 8. doi:10.1007/3-7643-7551-5. ISBN 978-3-7643-7551-5.

[1] Lémeray, E.-M. (1897). "Sur la convergence des substitutions uniformes" (PDF). Nouvelles annales de mathématiques, 3e série. 16: 306–319.

[stoop-2] Stoop, Ruedi; Steeb, Willi-Hans (2006). Berechenbares Chaos in dynamischen Systemen [Computable Chaos in dynamic systems] (in German). Birkhäuser Basel. p. 8. doi:10.1007/3-7643-7551-5. ISBN 978-3-7643-7551-5.

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