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