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Mathematical Function Plot 
Description 
Moebius Strip, 1 halfturn (n=1) 
Equation 
:

Coordinate System 
Cartesian ( Parametric Plot) 
u Range 
0 .. 4π 
v Range 
0 .. 0.3 
Mathematica Code

Please be aware that at the time of uploading (15:27, 19 June 2007 (UTC)), this code may take a significant amount of time to execute on a consumerlevel computer. 


This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found here. 

This code requires the following packages:
< MoebiusStrip[r_:1] =
Function[
{u, v, n},
r {Cos[u] + v Cos[n u/2]Cos[u],
Sin[u] + v Cos[n u/2]Sin[u],
v Sin[n u/2],
{EdgeForm[AbsoluteThickness[4]]}}];
aa[gr_] := Module[{siz, kersiz, ker, dat, as, ave, is, ar},
is = ImageSize /. Options[gr, ImageSize];
ar = AspectRatio /. Options[gr, AspectRatio];
If[! NumberQ[is], is = 288];
kersiz = 4;
img = ImportString[ExportString[gr, "PNG", ImageSize > (
is kersiz)], "PNG"];
siz = Reverse@Dimensions[img[[1, 1]]][[{1, 2}]];
ker = Table[N[1/kersiz^2], {kersiz}, {kersiz}];
dat = N[img[[1, 1]]];
as = Dimensions[dat];
ave = Partition[Transpose[Flatten[ListConvolve[ker, dat[[All, All, #]]]] \
& /@ Range[as[[3]]]], as[]  kersiz + 1];
ave = Take[ave, Sequence @@ ({1, Dimensions[ave][[#]],
kersiz} & /@ Range[Length[Dimensions[ave]]  1])];
Show[Graphics[Raster[ave, {{0, 0}, siz/kersiz}, {0, 255}, ColorFunction >
RGBColor]], PlotRange > {{0, siz[[1]]/kersiz}, {
0, siz[]/kersiz}}, ImageSize > is, AspectRatio > ar]
]
deg = 1;
gr = ParametricPlot3D[Evaluate[MoebiusStrip[][u, v, deg]],
{u, 0, 4π},
{v, 0, .3},
PlotPoints > {99, 3},
PlotRange > {{1.3, 1.3}, {1.3, 1.3}, {0.7, 0.7}},
Boxed > False,
Axes > False,
ImageSize > 220,
PlotRegion > {{0.22, 1.15}, {0.5, 1.4}},
DisplayFunction > Identity
];
finalgraphic = aa[gr];
Export["Moebius Surface " <> ToString[deg] <> ".png", finalgraphic]
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