Re: Mathematical Experiments

• To: mathgroup at smc.vnet.net
• Subject: [mg54803] Re: [mg54777] Mathematical Experiments
• From: DrBob <drbob at bigfoot.com>
• Date: Wed, 2 Mar 2005 01:26:50 -0500 (EST)
• References: <200503010658.BAA25222@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

```I have Needs["Graphics`"] in my Init file, so I thought I'd never need to manually load graphics packages like Graphics`ParametricPlot3D`.

Your examples proved me wrong. If I don't load that package, ParametricPlot3D works, but not with the 4-element ranges you've used below.

Including a step-size isn't necessary for most of your examples, but it is for the last one. It seems to hang up my machine if I leave it out, and even Pi/30 is too small for comfort.

Bobby

On Tue, 1 Mar 2005 01:58:39 -0500 (EST), Daniel Alayon Solarz <danieldaniel at gmail.com> wrote:

> I just wanted to share some minor graphical applications that came
> along with my research.  Try tweaking parameters and see what happens. Here are
> showed the 6 solutions of order 1,2,3. The other 6 are anti-solutions,
> is possible to figure out how to construct them. Enjoy.
>
> << Graphics`Animation`
> << Graphics`ParametricPlot3D`
> Animate[ParametricPlot3D[{(Log[Tan[v/2]] + t)*
>        Cos[u] Sin[v], (Log[Tan[v/2]] + t)*Sin[u] Sin[v],
> (Log[Tan[v/2]] + t)*
>        Cos[v]}, {u, -Pi, Pi, Pi/30}, {v, Pi/6, Pi/3, Pi/30}], {t,
> -Pi/8,
>    Pi/2}]
>
> << Graphics`Animation`
> << Graphics`ParametricPlot3D`
> Animate[ParametricPlot3D[{(u + t)*Cos[u] Sin[v], (u + t + 1)*
>        Sin[u] Sin[v], (u + t)*Cos[v]}, {u, -Pi, Pi, Pi/30}, {v, Pi/6,
> Pi/3,
>      Pi/30}], {t, -Pi, 4Pi/2}]
>
> << Graphics`Animation`
> Animate[ParametricPlot3D[{(2u*Log[Tan[v/2]] + t)*
>        Cos[u] Sin[v], (2u*Log[Tan[v/2]] + t)*
>        Sin[u] Sin[v], (2u*Log[Tan[v/2]] + t)*Cos[v]}, {u, -Pi, Pi,
>      Pi/20}, {v, Pi/3, Pi/2, Pi/20}], {t, -4Pi, 4Pi/2}]
>
> << Graphics`Animation`
> Animate[ParametricPlot3D[{(u^ 2 - Log[2Tan[v/2]] + t)*
>        Cos[u] Sin[v], (u^2 - Log[2Tan[v/2]] + t)*
>        Sin[u] Sin[v], (u^2 - Log[2Tan[v/2]] + t)*Cos[v]}, {u, -Pi,
> Pi,
>      Pi/30}, {v, Pi/4, Pi/2, Pi/30}], {t, -4Pi, 4Pi}]
>
> << Graphics`Animation`
> Animate[ParametricPlot3D[{(u^ 3 - 3u*Log[2Tan[v/2]] + t)*
>        Cos[u] Sin[v], (u^ 3 - 3u*Log[2Tan[v/2]] + t)*
>        Sin[u] Sin[v], (u^ 3 - 3u*Log[2Tan[v/2]] + t)*Cos[v]}, {u,
> -Pi, Pi,
>      Pi/30}, {v, Pi/4, Pi/2, Pi/30}], {t, -4Pi, 4Pi}]
>
> << Graphics`Animation`
> Animate[ParametricPlot3D[{(3u^ 2*Log[2Tan[v/2]] - Log[3Tan[v/2]] + t)*
>        Cos[u] Sin[v], (3u^ 2*Log[2Tan[v/2]] - Log[3Tan[v/2]] + t)*
>        Sin[u] Sin[v], (3u^ 2*Log[2Tan[v/2]] - Log[3Tan[v/2]] + t)*
>        Cos[v]}, {u, -Pi, Pi, Pi/30}, {v, Pi/3, Pi/2, Pi/30}], {t,
> -4Pi, 4Pi}]
>
> Regards
> Daniel
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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