Uploaded March 2022 | Updated September 2026, 1 week ago
An epicycle is a curve generated by tracing a circle as its center rotates around another circle. More and more complex curves can be generated by adding more and more circles, each with different radii, frequencies, and starting angles. In fact, any path in the plane can be approximated with enough circles stacked on each other in this way.
In this video, I use a datapack to trace out these curves in Minecraft. Each spawn egg contains all the information required for tracing out the curves, which is just a list of radii, rotation frequencies, and starting angles.
You can download the datapack from my GitHub here: github.com/DqwertyC/epicycles-datapack
Want to make your own epicycle generated curves? Use my epicycle webtoy to generate give commands for spawn eggs compatible with this datapack: dqwertyc.github.io/epicycles-webtoy
Check out this 3Blue1Brown video on Fourier series for an in depth explanation behind how this works: youtube.com/watch?v=r6sGWTCMz2k
Happy pi day!
An epicycle is a curve generated by tracing a circle as its center rotates around another circle. More and more complex curves can be generated by adding more and more circles, each with different radii, frequencies, and starting angles. In fact, any path in the plane can be approximated with enough circles stacked on each other in this way.
In this video, I use a datapack to trace out these curves in Minecraft. Each spawn egg contains all the information required for tracing out the curves, which is just a list of radii, rotation frequencies, and starting angles.
You can download the datapack from my GitHub here: github.com/DqwertyC/epicycles-datapack
Want to make your own epicycle generated curves? Use my epicycle webtoy to generate give commands for spawn eggs compatible with this datapack: dqwertyc.github.io/epicycles-webtoy
Check out this 3Blue1Brown video on Fourier series for an in depth explanation behind how this works: youtube.com/watch?v=r6sGWTCMz2k
Happy pi day!
