Summary

Polykite aperiodic monotile.

My contribution to the recently discovered "tile" has a complex curving pattern that generates a cool design when assembled.

The unique thing about my pattern is that it generates a groove that is continuous and fully connected to all other grooves. There are no closed loop regions.

Designed with chamfers to print without support material.

I'd suggest one filament color for the bottom few layers... then swap to another color for the middle... and then switch to another color for the top layers.
Alternatively, you might print these in one color and then paint the groove later.

These tiles need to have patterns on both sides because the aperiodic pattern requires a tile to flip upside down occasionally.

This continuous curve is interesting... Maybe it could have an application in modular micro-fluidics someday?

Added a single sided version for both sides. This version looks better than the double sided version, as the "top" surface of the print is always up when assembled. Ratio of two sides is roughly 1:7.