I'm trying to plot two recursive functions (p and θ) on a map. So far I have:
θ0 = Pi/2;
p0 = 0;
α = 0.1;
β = 1;
θ[j_] := θ[j] = θ[j - 1] + β*p[j - 1];
p[j_] := p[j] =
p[j - 1] - α*Sin[θ[j - 1] + β*p[j - 1]];
θ[0] = θ0;
p[0] = p0;
How can I plot p[j]
against θ[j]
for 0 <= j <= 100
?
Answer
I think you are looking for DiscretePlot
:
DiscretePlot[{θ[j], p[j]}, {j, 0, 100}]
Or perhaps you want something like this?:
ListPlot @ Table[{θ[j], p[j]}, {j, 0, 100}]
Another method is to use ParametricPlot
after sufficiently coercing the input, e.g.:
f[x_?NumericQ] := {θ[#], p[#]} & @ Round @ x
ParametricPlot[f[j], {j, 0, 100}]
(Aspect ratio may be controlled with the AspectRatio
option.)
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