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 ClickRecurrenceMap2D (1.0.0) current version: 2.1.1 »

Source Notebook

Get the orbits of a planar map in an interactive way using a clickable panel

Contributed by: E. Chan-López, Erika Yuridia Flores Chan, Héctor Argote Morales & Víctor Castellanos

ResourceFunction["ClickRecurrenceMap2D"][map,depvars,trange]

gives the orbits corresponding to the recurrence equations represented by map, the dependent variables depvars, a vector trange including the minimum and maximum number of iterations by clicking in an interactive panel.

Details and Options

The map must be a list of recurrence equations.
The depvars must be a list containing the dependent variables.
The trange must be a list containing the minimum and maximum number of iterations.
ResourceFunction["ClickRecurrenceMap2D"][map,depvars,trange] obtains initial condition data from points the user clicks and plots the corresponding orbits.
ResourceFunction["ClickRecurrenceMap2D"][map,depvars,trange] takes the same options as ListPlot.

Examples

Basic Examples (1) 

Generate the orbit of the Gingerbreadman map and visualize it:

In[1]:=
Gingerbreadman[{x_[n_], y_[n_]}] := {x[n + 1] == 1 - y[n] + Abs[x[n]], y[n + 1] == x[n]}; ResourceFunction["ClickRecurrenceMap2D", ResourceVersion->"1.0.0", ResourceSystemBase -> "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"][Gingerbreadman[X], {x[n], y[n]}, {1, 10000}, PlotStyle -> {{Black, PointSize[0.003]}}]
Out[2]=

Scope (2) 

Gumowski-Mira Attractor (2) 

Generate some orbits of the Gumowski-Mira map:

In[3]:=
f[x_[n_]][a_] := a x[n] + (2 (1 - a) x[n]^2)/(1 + x[n]^2)^2; GMAttractor[{x_[n_], y_[n_]}][{a_, b_}] := {x[n + 1] == b y[n] + a x[n] + (2 (1 - a) x[n]^2)/(1 + x[n]^2)^2, y[n + 1] == ReplaceAll[ x[n] -> b y[n] + a x[n] + (2 (1 - a) x[n]^2)/(1 + x[n]^2)^2][ f[x[n]][a]] - x[n]}; X = {x[n], y[n]}
Out[5]=

Visualize the orbits by clicking:

In[6]:=
ResourceFunction["ClickRecurrenceMap2D", ResourceVersion->"1.0.0", ResourceSystemBase -> "https://www.wolframcloud.com/objects/resourcesystem/api/1.0"][GMAttractor[X][{0.266, 1}], X, {1, 1500}, PlotStyle -> PointSize[0.003]]
Out[6]=

Publisher

Ramón Eduardo Chan López

Version History

  • 2.1.1 – 02 October 2023
  • 2.1.0 – 05 July 2023
  • 2.0.0 – 31 May 2023
  • 1.1.0 – 27 March 2023
  • 1.0.0 – 16 September 2022

Source Metadata

  • Citation:
    • Alligood, K.T., Sauer, T.D., Yorke, J.A. (1997). Chaos in Two-Dimensional Maps. In: Chaos. Textbooks in Mathematical Sciences. Springer, Berlin, Heidelberg. DOI: 10.1007/978-3-642-59281-2_5
    • Schuster, H. G., & Just, W. (2006). Deterministic chaos: an introduction. John Wiley & Sons. DOI:10.1002/3527604804
    • Moon, F. C. (2008). Chaotic and fractal dynamics: introduction for applied scientists and engineers. John Wiley & Sons. DOI:10.1002/9783527617500

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