Directed alternating lattices and the site-to-bond ratio for animals and trees

We present here a brief summary of results on so-called «exotic» directed lattices having nonregular periodicity. Such lattices, e.g., the Archimedean nets, are characterized by different site types and a spread of coordination numbers. The evidence adduced here shows that the exponent structure for the growth of animals and trees on such lattices is of the form predicted, with θ 0 for trees equivalent to θ for unrestricted animals, independent of the periodicity property. This supports the general form θ c =θ 0 -c, for cycles c=0