Tulips: versions for logo of International Mathematica Symposium, Maastricht, June 20-24, 2008.

Official Version

r[u_,v_,c_]=v^(1.5) (1-u^2/8)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v],
r[u,v,c] Cos[u]*Cos[v],
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0,2Pi/4},{v,0, Pi 0.76},
BoxRatios->{1,1,1.3},
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
ColorFunction -> (ColorData[
     "SolarColors"][(1 - Sqrt[#1^2 + #2^2]/4)^0.7] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,1.}]

Official Version with lower resolution

r[u_,v_,c_]=v^(1.5) (1-u^2/8)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
r[u,v,c] Cos[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0,2Pi/4},{v,0, Pi 0.76},
BoxRatios->{1,1,1.3},
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
ColorFunction -> (ColorData[
     "SolarColors"][(1 - Sqrt[#1^2 + #2^2]/4)^0.7] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,1.}]

Version 2

r[u_,v_,c_]=v^(1.5) (1-u^2/8)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
r[u,v,c] Cos[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0,2Pi/4},{v,0, Pi 0.76},
BoxRatios->Automatic,
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
 ColorFunction -> (ColorData[ "SunsetColors"][
       Sin[2((#1^2 + #2^2)/18)^1.5]/1.5] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,0.8}]

Version 2 with higher resolution

r[u_,v_,c_]=v^(1.5) (1-u^2/15)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v],
r[u,v,c] Cos[u]*Cos[v],
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0.1,2Pi/4-0.1},{v,0, Pi 0.76},
BoxRatios->Automatic,
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
 ColorFunction -> (ColorData[ "SunsetColors"][
       Sin[2((#1^2 + #2^2)/18)^1.5]/1.5] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,0.9}]

Version 3

r[u_,v_,c_]=v^(1.5) (1-u^2/8)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
r[u,v,c] Cos[u]*Cos[v](1+0.05 Sin[6 c (u)]^4),
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0,2Pi/4},{v,0, Pi 0.76},
BoxRatios->{1,1,1.3},
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
ColorFunction -> (ColorData[ "SunsetColors"][
       Sin[0.2+((#1^2 + #2^2))^2/35]/1.5] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,1.}]

Version 3 with higher resolution

r[u_,v_,c_]=v^(1.5) (1-u^2/8)(0.5+(0.03+Abs[Sin[c u/2]] )^(1/5));
jazmin[u_,v_,c_]=Evaluate[
{r[u,v,c] Sin[u]*Cos[v],
r[u,v,c] Cos[u]*Cos[v],
1.2  r[u,v,c]^0.1( 3 Abs[Sin[2v]]^(8) (0.5+Abs[Sin[c u/2]]^0.5)) 
}];

leaf=ParametricPlot3D[
Evaluate[jazmin[u,v,4]], {u,0.05,2Pi/4-0.05},{v,0, Pi 0.76},
BoxRatios->{1,1,1.3},
 PlotRange->All,Boxed->False,Axes->None,Mesh->False,PlotPoints->10,
ColorFunction -> (ColorData[ "SunsetColors"][
       Sin[0.2+((#1^2 + #2^2))^2/35]/1.5] &), ColorFunctionScaling -> False]

MMz[α_]:=(({{Cos[α], Sin[α], 0}, {-Sin[α], Cos[α], 0}, {0, 0, 1}}));

tulip=Table[leaf/.
GraphicsComplex[u_,v___]:>
GraphicsComplex[u/.{a_,b_,c_}:>MMz[α].{a,b,c},v],{α,0,2Pi,Pi/3}];

Show[tulip,PlotRange->All,BoxRatios->{1,1,1.}]