Inspired by the work of Michael Fogleman and a blog post by tobiastoft, I got myself an old HP 7550A plotter and a collection of “fresh” pens from ebay.

Fresh plotter pens

Getting it to work was a little tricky, but the quality of the drawings is impressive (0.025mm accuracy) considering that the device was build some 30 years ago.

Because I like reinventing wheels and need a project to learn rust, I’m trying to write the image generation and controlling software myself. Below are some of the first results, images of Appolonian Gaskets with different starting configurations.

If you are intrested in math, make sure to check out the second post on Math Less Traveled on this topic, the way Descartes’ Theorem works for the product of the curvature and the center is fascinating.

Appolonian Gasket, (-1, 2, 2, 3) Appolonian Gasket, (-2, 3, 6, 7) Appolonian Gasket, (-4, 8, 9, 9)

The images were drawn using the best pen I could find so far, a “Dia-Nielsen Technograph” drafting pen with a 0.25mm tip.

On the software side, one of the challenges is to reorder the objects in a way that reduces motions of the plotter head, a variation of the Traveling Salesman Problem.

In the left image, all circles were drawn in the order they were created. In the right one their order was chosen using a greedy search, reducing the distance traveled by a factor of five.

Appolonian Gasket, (-1, 2, 2, 3), paths
before Appolonian Gasket, (-1, 2, 2, 3), paths
after