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Mathematical Experiments


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


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