Multifractality to Photonic Crystal {\&} Self-Organization to Metamaterials through Anderson Localizations {\&} Group/Gauge Theory

Arthur Cayley at least investigate by creating the theory of permutation group[F:$\backslash \backslash $Group\textunderscore theory.htm] where in cell elements addressing of the lattice Qmf used a Cayley tree, the self-afine object Qmf is described by the combination of the finite groups of rotation {\&} inversion and the infinite groups of translation {\&} dilation[G Corso {\&} LS Lacena: \textbf{``Multifractal lattice and group theory'', } Physica A: Statistical Mechanics {\&}Its Applications, \textbf{2005 }, v 357, issue I, h 64-70; http://www.sciencedirect.com/science/articel/pii/S0378437105005005 ] hence multifractal can be related to group theory.