while going through my old University notes, I discovered this nice function.

A college of mine (hi Michael!) wanted to build a function which forms a heart and this is our result.

Obviously, a function cannot do this as you have multiple $y$-values for one $x$-value but combining two functions in two regimes, you can get close ( it is still missing that the first derivative must converge agains $\pm \infty$ for $x=\pm 1$).

Here is the result: