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RE: Art Graphics in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg35252] RE: [mg35244] Art Graphics in Mathematica
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 5 Jul 2002 02:18:49 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: Thiery Balser [mailto:strichpunkt2 at gmx.net]
To: mathgroup at smc.vnet.net
> Sent: Wednesday, July 03, 2002 11:16 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg35252] [mg35244] Art Graphics in Mathematica
> 
> 
> Hi,
> 
> 
> I've just found an amazing site with really astonishing 
> picutres apparently
> generated by mathematica..
> 
> There are even the formulas on this site (please see below), 
> but I have no
> clue, what sort of Plot this formula requires.
> 
> http://silver.szote.u-szeged.hu/math/Gallery/Creatures/crea.html
> 
> Any hint is highly appreciated,
> 
> Regards,
> Thiery
> 
> 
> 

Thiery,

since this is art, it's a matter trial, patience and phantasy. I would try
(I shortly did, but lack the patience) something like, e.g.

ParametricPlot3D[{Sin[u]*Cos[v], Cos[u]*Cos[v], 
      Sin[2v], {EdgeForm[], Hue[=some function of v=]}}, {u, -Pi*3/4, 
      Pi*3/4}, {v, -Pi/2, Pi/2}, Axes -> False, Boxed -> False, 
    Background -> GrayLevel[0], Lighting -> False, 
    PlotPoints -> 100] // Timing

To reverse engineneer that =some function of v= (or of u or both), observe
how u varies along the polygons, try to guess the argument to Hue (best make
a plot), find the most "simple" function that approximately matches your
guesses, then fine tune the parameters by visual appearance. The art is not
to spend (or perhaps just to spend) a lifetime.

For guesses of a "simple" function follow the complexity of the function
itself, for the example here try simple algebraic expressions of v, Sin[v],
Cos[v],... 
Hue[1/3 - Sin[v^2]^2] just isn't it (it lacks certain obvious properties),
but may explain that approach.

--
Hartmut