I have a vague memory of a math worksheet in middle school that required drawing lines with a straightedge, and together lines produced something like a hyperbolic curve:
To me these looked like early 3D computer graphics.
I don't remember what all the worksheet explored, but I do remember exploring on my own in moments of boredom. The simplest evolutions are making the base axes different lengths or angling them relative to each other:
Axes can be joined together:
There's no reason lines from different axes can't overlap:
And there's no reason the axes have to join together at their ends, though disconnecting them does unravel the grid at the fringes:
Of course, there's nothing sophisticated about these, but they do serve as doodle material in long meetings, having enough complexity to occupy one's hands but not enough to distract the brain from listening.
Update November 2023: The curves formed by these constructions are quadratic Bézier curves.