Using the recipe of the last post for four-dimensional space (p=4) I got this image of 8-fold rotational symmetry:

A center of approximate 8-fold rotational symmetry is near the lower left corner. Large brown patches appear at roughly equal distances. They lie at corners of squares, rhombs with an acute angle of 45 degrees and regular octagons. These polygons bear similar decorations. Overall this image seems to be an approximate decoration of the Ammann-Beenker tiling. This is no surprise as a simple superposition of sinusoidal waves too makes a decoration of the Ammann-Beenker tiling, see my post “Quasiperiodic pattern from eight waves and the Ammann-Beenker tiling”.

To do your own experiments, simply get my public repository https://github.com/PeterStampfli/creatingSymmetries and first have a look at “warpingKaleidoscope.html”, which you can open in your browser to create kaleidoscopic images. But beware, everything is changing. The current commit is 929315b.