In the mathematical sense, this is is not a kaleidoscope but a conformal mapping. What they have in common with a kaleidoscope are the distortions that lead to symmetries.
(p^c-1)/(p^c+1)
This mapping (distortions of the image plane) is calculated with complex numbers. Where p are the pixel coordinates and c is a constant.
This one is from a walk in the park, where I took a photo of grass with raindrops on it.
I made a 42-fold, rotating mandala from it, used that in another 8-fold mandala and mixed it into a color filter.