彩虹蝴蝶酥

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启动Mathematica

制作蝴蝶酥原料。需要解一个组非线性微分方程。输入下列代码并 Shift+Enter.
sol[v_, a0_, x0_, y0_, z0_] :=
NDSolve[{x'[t] == - v x[t] + y[t] z[t],
  y'[t] == -v y[t] + ( z[t] - a0) x[t], z'[t] == 1 - x[t] y[t],
  x[0] == x0, y[0] == y0, z[0] == z0}, {x, y, z}, {t, 0, 200},
 MaxSteps -> Infinity]

焙制蝴蝶酥，并上色。输入下列代码并 Shift+Enter.
ParametricPlot3D[
Evaluate[{x[t], y[t], z[t]} /. sol[0.8, 1.55, 0, 1, 0]], {t, 0, 200},
 ColorFunction -> (ColorData["Rainbow"][#4] &), PlotStyle -> {Thick},
 SphericalRegion -> True, ImageSize -> 500 {1, 1},
PlotRange -> {{-4, 5}, {-4, 4}, {-0.5, 10}}, Boxed -> False,
Axes -> None, PerformanceGoal -> "Quality"]