LiveGraphics3D Example:
A Butterfly

Simple Version
 This plot shows the function (cos(s), sin(s), 0.5) (exp(cos(s)) - 2cos(4s) + sin(s / 12)^5) with s ranging from -1.57 to 4.71. A two-dimensional version of this butterfly curve is given in Stan Wagon's book "Mathematica in Action".

Colored Version
 Same data, different visualization.

Implementation

Here is how to create these graphics within Mathematica:

tab1=Table[
{Cos[s],Sin[s],0.5}*(Exp[Cos[s]]-2Cos[4 s]+Sin[s/12]^5),
{s,-Pi/2.,2.Pi-Pi/2.+0.01,2Pi/100.}];
g=Show[Graphics3D[Line[tab1]],Axes->True,
ViewPoint->{0,0,2},ViewVertical->{1,0,0},
AxesLable->{x,y,z}]

This will produce the simple version. The colored version is produced by:

tab2=Table[{Hue[N[i/Length[tab1]]],
Polygon[{{0,0,0},tab1[[i]],tab1[[i+1]]}]},
{i,1,Length[tab1]-1}];
g=Show[Graphics3D[{EdgeForm[],tab2},Lighting->False,
Boxed->False,ViewPoint->{-0.416,1.290, 0.974},
ViewVertical->{0.632, -0.389, 1.518}]];

The procedure to use the Graphics3D object with LiveGraphics3D is explained in the documentation.

Martin Kraus, April 15, 2021