Cobweb plot

A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map.

[1] Using a cobweb plot, it is possible to infer the long-term status of an initial condition under repeated application of a map.

On the Lémeray diagram, a stable fixed point corresponds to the segment of the staircase with progressively decreasing stair lengths or to an inward spiral, while an unstable fixed point is the segment of the staircase with growing stairs or an outward spiral.

line crosses the function graph.

A period-2 orbit is represented by a rectangle, while greater period cycles produce further, more complex closed loops.

A chaotic orbit would show a "filled-out" area, indicating an infinite number of non-repeating values.

Construction of a cobweb plot of the logistic map , showing an attracting fixed point .
An animated cobweb diagram of the logistic map , showing chaotic behaviour for most values of .