Multifractality in rotational percolation models

In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable si is assigned to each lattice site whose value corresponds to the number times it has been visited during the growth of a cluster. It is proposed here that the percolation transition and the multifractal aspects of infinite percolation clusters under rotational constraint can be studied defining suitable measures in terms of the state variable si. This method does not require to introduce any external agency like an electric current or a random walker in order to explore multifractality as in the case of ordinary percolation. The state variable representation also describes the universality class of the percolation models appropriately.