TITLE: Drawing heart in mathematica
QUESTION [14 upvotes]: It's not really a typical math question. Today, while studying graphs, I suddenly got inquisitive about whether there exists a function that could possibly draw a heart-shaped graph. Out of sheer curiosity, I clicked on Google, which took me to this page.
The page seems informative, and I am glad to learn certain new things! Now I am interested in drawing them by my own using Mathematica. So my question is: is it possible to draw them in Mathematica? If yes, please show me how.

REPLY [2 votes]: A three-dimensional space curve with the shape of a red heart:

The Mathematica code for the image above is:
ParametricPlot3D[{Cos[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u]), v, 
  Sin[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u])}, 
   {u, -Pi, Pi}, {v, -1, 1}, Axes -> None, Mesh -> False, 
 Boxed -> False, 
   PlotStyle -> {Red, Specularity[White, 10]}]

3D red heart with Mesh and lines:

Mathematica code for the image above:
ParametricPlot3D[{Cos[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u]), v, 
  Sin[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u])}, {u, -Pi, 
  Pi}, {v, -0.97, 0.97}, PlotPoints -> 50, Axes -> None, 
 Boxed -> False, 
 PlotStyle -> 
  Directive[Glow[Red], Specularity[White, 30], Opacity[0.15]], 
 Mesh -> 50, Background -> Black, MeshStyle -> {Blue, Red}, 
 Lighting -> {{"Directional", Yellow, {{1.5, 1.5, 5}, {1.5, 1.5, 0}}, 
    Pi/6}}]

A variation on the use of the Taubin heart surface with hue:

Mathematica code for the last image above:
ContourPlot3D[(-1/10) x^2 z^3 - 
   y^2 z^3 + (2 x^2 + y^2 + z^2 - 1)^3 == 0, {x, -1.2, 1.2}, {y, -1.4,
   1.4}, {z, -1.5, 1.5}, Mesh -> False, PlotPoints -> 60, 
 Axes -> None, Boxed -> False, 
 ContourStyle -> Directive[Opacity[0.5], Red], 
 ColorFunction -> Function[{x, y, z, f}, Hue[z]]]

For more customized heart images, see the post in my website/blog:
https://knowledgemix.wordpress.com/2014/02/14/heart-to-heart-with-3d-math/