Here is a plot corresponding to the computation for the first 1124 sequence of the average of over all quadruples such that (Note: to cut the computation time I’ve only taken those with and , this without loss of generality, thanks to the commutativity of the quadruple product which doesn’t care about the order and to the additivity of the average) (click to enlarge).
Here is the final plot. Note the change of axis, I prefer now to plot as a function of each time . (click to enlarge)
Below are previous plots just for the record.
After running a while longer :