# VectorPlot or StreamPlot on a simplex

**URL:** <https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231>\
**Category:** Questions\
**Tags:** mathematica, graphics-and-visualization\
**Created:** [March 25, 2015, 11:50am UTC](https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231 "2015-03-25T11:50:45Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![clmnsbchn](https://avatars.discourse-cdn.com/v4/letter/c/74df32/32.png) [@clmnsbchn](https://community.wolfram.com/u/clmnsbchn)\
**Post date:** [March 25, 2015, 11:50am UTC](https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231/1 "2015-03-25T11:50:45Z")

</div>

Hello,

I want to plot the solution to a system of the form

```
x'[t] == f[x,y,z,t]

y'[t] == g[x,y,z,t]

z'[t] == h[x,y,z,t]

```

in a triangular simplex, because `x+y+z=1` and `x>=0,y>=0 and z>=0`.

Any ideas how to do that? I tried Vectorplot3D with a RegionPlot, but the resulting plot is not very compelling.

Thanks a lot for any help on this?

Clem

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**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [March 25, 2015, 12:45pm UTC](https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231/2 "2015-03-25T12:45:08Z")

</div>

You can try the free package CurvesGraphics6, available from [http://www.dimi.uniud.it/gorni/Mma](http://www.dimi.uniud.it/gorni/Mma)  
About half way through the page you will see an example of stream lines on a surface.

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<div class="post-metadata">

**Author:** ![clmnsbchn](https://avatars.discourse-cdn.com/v4/letter/c/74df32/32.png) [@clmnsbchn](https://community.wolfram.com/u/clmnsbchn)\
**Post date:** [March 25, 2015, 1:08pm UTC](https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231/3 "2015-03-25T13:08:56Z")

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Thanks, Gianluca, I will look into that.

I meant something like in the following graph:

 ![Koz3AP0.png](https://global.discourse-cdn.com/wolfram/original/3X/5/5/5540949227007d0680151c964567c1d23fc48848.png)

C

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<div class="post-metadata">

**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [March 25, 2015, 1:33pm UTC](https://community.wolfram.com/t/vectorplot-or-streamplot-on-a-simplex/5231/4 "2015-03-25T13:33:40Z")

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With the package and the code

```
region = DiscretizeRegion[Triangle[{{0, 0}, {1, 0}, {0, 1}}]];
PlotCurveOnSurface3D[{{x, y, 1 - x - y}, {x, y} \[Element] region},
 {{x, y}, {x, y} \[Element] region}]

```

you get the attached picture.