Summary

Kaleidoscopes of three mirrors can have any rotational symmetries at the three corners if we allow for circle arcs as sides.

At circle arcs we use inversion as a generalization of mirror images.

We have an efficient iterative method for generating these images.

We get periodic images in elliptic (spherical), Euclidic or hyperbolic space.

These images are decorations of regular tilings except for rosettes in elliptic geometry.

To get good images we need pixel averaging and interpolation.

All can be done rapidly. I am using plain vanilla javascript and an average laptop.

Create your own images with the app at geometricolor.ch!

With additional mirrors this app makes decorations of semi-regular tilings.