Tamari Attractor

Author

Eric W. Weisstein
August 31, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/DynamicalSystems/TamariAttractor.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/TamariAttractor.

Copyright 2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

A trajectory of the Tamari system after discarding the initial transient.

Module[{solution,a,b,c,d,e,f,g,u,i},{a,b,c,d,e,f,g,u,i}={1.013,-0.021,0.019,0.96,0,0.01,1,0.05,0.05};solution=NDSolveValue[{x'[t]==(x[t]-a y[t]) Cos[z[t]]-b y[t] Sin[z[t]],y'[t]==(x[t]+c y[t]) Sin[z[t]]+d y[t] Cos[z[t]],z'[t]==e+f z[t]+g a ArcTan[(((1-u) x[t] y[t])/(1-i))],x[0]==0.9,y[0]==1,z[0]==1},{x,y,z},{t,0,800}];ParametricPlot3D[Through[solution[t]],{t,100,800},PlotPoints->1000,PlotStyle->Orange,Axes->False,Boxed->False,Method->{"ShrinkWrap"->True}]]