Spirograph is a classic geometric drawing toy, developed 50 years ago and still popular today.
Normally it involves using multiple gears to draw intricate patterns on sheets of paper, but if that sounds like too much hassle then you could just download the open source (and entirely unofficial) Spirograph for your PC.
The program is implausibly tiny -- a 97.1KB download? really? -- and so it’s no surprise that the interface is, well, basic: a blank work area and a panel crammed with buttons, boxes, and seed values.
It’s not exactly clear how to get started, but opening an example offers some clues. Try "ThreeCurves" and three tabs appear, showing that the design is comprised of three separate elements. Each of these has its own separate starting values which you can view by clicking that tab.
These values can be freely tweaked to change the pattern. Increasing “Stator Radius” by just a point or two can have dramatic effects, so that’s a good place to begin.
Once you’ve played around with the examples, you’ll be ready to create something new of your own. Click File > New to clear any existing design, then the Add button and an initial pattern appears. Tweak this as before, then click Add to overlay another pattern. Set new color and opacity values, maybe experiment with Fill Modes, or use the Animate feature to show your design being drawn from scratch.
When you’re happy, patterns can be copied to the clipboard, or saved as images in various formats (PNG, GIF, TIFF, BMP and JPG).
Spirograph could be easier to learn. And it’ll probably have to be renamed once the trademark holders notice its existence. But if you enjoy fractal explorers and similar math-based pattern generators then it should keep you entertained for an hour or two.