Rotating Apollonian Gasket Pattern

Hellooo!! This was a short 1 day project that came up in my head while watching a video on complex complex shapes made by ThoughtThrill that so happened to match up well with this contest.

Check out his video!

Here I 3D printed an Apollonian Gasket at which it can rotate, acting as a rotating platform. For those wondering what exactly an Apollonian Gasket is, it is a type of fractal discovered by Ancient greek Mathematician Apollonius of Perga. The pattern comes from the fact that with three circles that are tangent to the other circles, they can have another circle that are tangent to the rest. This in turn creates another set of circles that can have another circle tangent to them. In other words, it is an infinite pattern that can create a number of beautiful imagery (go lookup online theres a ton!). Due to the fact that these are being 3D printed unfortunately, I had to limit the amount of circles I can have lol.

1. Access to a 3D printer
2. Filament of some kind
3. 608-RS Ball Bearing
4. Printer (if you want to add printed designs on your print)

Designing a pattern for an Apollonian Gasket is relatively simple, however may take some time depending on the amount of circles you want. To start, you have three circles of whatever size that are tangent to each other, but do not have a single point where they are all tangent to each other. From here, a circle can be made that are tangent to all three of those circles whether it is in between the 3 circles or on the outside. After that, that is all you need! The process can be repeated to continually create a more complex pattern to your liking.

After making the pattern, I made a simple platform that the Apollonian Gasket can assemble with via a bearing to create rotation.

For 3D printing, one can use any filament they want. However, one warning I would like to give is to check in the slicer to see if your Apollonian Gasket is able to print as it could be a huge waste of time with how long it takes to print these complex shapes.

After 3D printing, the bearing can be simply pushed in and the two parts can connect. Here are the files!

One improvement that I did not have enough time to get on is printing designs that can be glued on to the circles (My printer is goofed right now D:< ). Though this is not necessary it would be a really cool and entertaining addition.