       Re: ParametricPlot Remark

• To: mathgroup at smc.vnet.net
• Subject: [mg7203] Re: [mg7177] ParametricPlot Remark
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Fri, 16 May 1997 02:30:34 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> ParametricPlot  - works fine giving nice smooth courbes ,
> ParametricPlot3D - samples largely giving a pretty zigzag form !

curve is bending more.
ParametricPlot3D is not adaptive -- it just uses the initial sample
points.

You can, as you observe, increase the number of sample points
(PlotPoints -> ...), but with your example  - plotting the solution
to the Lorentz equations - you have interpolating functions, which
*have* been constructed adaptively, and we can extract the points
found.

s = 10;
b = 8/3;
r = 167;

tmax = 10;

eq = {
x'[t] == s ( y[t] - x[t] ),
y'[t] == r x[t] - y[t] - x[t] z[t],
z'[t] == - b z[t] + x[t] y[t],
x == 0,
y == 1,
z == 0
};

sol = NDSolve[ eq, {x,y,z} , {t, 0, tmax},
MaxSteps -> 5000, StartingStepSize -> 0.001];

2) get the coordinates of the points found

coordinates =

3) Plot the line through the points

Show[Graphics3D[Line[coordinates]]]

Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk/

```

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