I'm interested in creating a Cayley's table of square using Mathematica. I'm not a programmer but occasionally resort to using Mathematica to simplify my work insofar as the programming doesn't take too long to create. I am after all a student and with a tight schedule as an undergrad in phys and math.
The idea behind the Cayley's table is this:
Imagine a square with with it's side labelled A,B,C,D. The possible permutations are all degrees of rotations (but which we will only restrict ourself to 0,90,180,270 and 360.Then, comes horizontal imaging, vertical imaging and diagonal imagine. (reflection)
The columns denotes some initial starting position and the rows denotes the machinery or function(or degrees of freedom) in which the initial position is subject to. What I want to achieve is be able to input an initial position and function such that mathematica will generate the output visually. Imagine holding a 2D square with the sides labelled A, B, C and D in clockwise motion and if a command was given to rotate the square by 90 degrees, there would be a corresponding change in the positions of the label. Extend this to reflection along the horizontal, vertical and diagonal axis.
An example is as below. Could anyone point to me the direction to get this started? Note: As it stands, I have no idea which tag should this topic go under.