Algebraic Hearts

One of the marvels of mathematics is the way in which an austere equation can unexpectedly blossom into an appealing geometric shape when represented graphically.

Cardioid.
Picture of an algebraic heart. Gabriel Taubin
A heart surface colored according to Gaussian curvature (left) and direction (right). Michael Trott/Wolfram Research
A heart-y prime puzzle. Ed Pegg Jr.

I can still recall experiencing such a sense of wonder when, decades ago, I first learned about polar coordinates in a high-school trigonometry class.