In most of the experiments below I have departed from a strictly symmetrical outcome because I prefer a small amount of disorder.
The transformation is programmed as specified in the Creating Symmetry book for a 3-fold rotation and translation, except that it also allows the final transformation function to include an addition that maps the colour map (source) plane directly to the output (target) plane, one-to-one. Note that the strict rotational symmetry would only be apparent if we rescaled all the images to be exactly the same width as height. (That is, the transformation functions are defined in a coordinate system that varies both width and height in the range (-1,1) regardless of the original image dimensions.)
In the default initial state of the program, the transformation is entirely one-to-one with no additional symmetry component. The amplitude of the one-to-one component can be reduced by multiplying by a scale factor between 1 and 0. Similarly the amplitude of the function that respects the three-fold rotation + translation symmetry can be increased by user manipulation of the program's control inputs.
The results below are the outcome of a experimenting with different balances between complete symmetry and some non-symmetrical additional.
Images inspired by the book Creating Symmetry.
