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Frierson used a powerful parameterization of the pattern of the order 3associative magic square to construct a family of six related order 9 compound(or composite) magic squares, several of them ancient. Stimulated by Bellew's1997 extension to order 27, we extend these ideas to all orders that are powersof 3, and in addition find simple formulae for the matrix spectra and entropicmeasures for all those orders. This construction is fractal and we givenumerical results to order 243 which show an information entropy measureconverging to a constant value of about 1.168.. for the lowest entropy members.We also briefly consider compounding of an order 4 magic square with the lowestentropy, for which we find a similar trend to constant entropy.

Frierson's 1907 Parameterization of Compound Magic Squares Extended to Orders 3^{l}, l=1,2,3,..., with Information Entropy