Graph of infinity

Question

Create a function that plots the $\infty$ symbol when plotted.

My function is $$|y|=|\sin x|$$ For $\{x: -3\le x \le 3\}$

Bonus points if your function is NOT mathematically equivalent to mine.

Double bonus points if the function is simpler than mine, or draws a more beautiful symbol.

Answer 1

Viviani's Curve is a nice way to see the infinity in a 3 dimensional figure by intersecting a sphere of radius $2a$ with a cylinder of centered at $(a,0,0)$ of radius $a$ this intersection:

$$V(t)=\bigg < a(1+ \cos(t)), a\sin(t), 2a\sin\Big(\frac t2\Big)\bigg>$$

Answer 2

Take any smooth, concave curve which passes through the origin at a finite, positive slope, then has a vertical tangent at its next root, for example $y = x \sqrt{1-x}$:

Then mirror it along both axes to complete an infinity-like sign e.g. $|y| = |x| \sqrt{1-|x|}$: