The fractal dimension of cluster perimeters generated by a kinetic walk

The fractal dimension d G of cluster perimeters generated by a recently proposed 'butterfly' growth walk is considered. In the long-range limit of the walk on a percolation cluster, d G appears to be equal to the fractal dimension of the singly connected bonds: d G =1/ nu . The new relation for chemical dimension d l is proposed: d l =d f /(d f -d G ). In the short-range limit the 'butterfly' walk on a Euclidean lattice appears to be in the same universality class as a random walk. The dynamic aspect of the growth walk is discussed and the continuously tunable spectral dimension is obtained. Both short- and long-range limits of this diffusion process are different from a random diffusion on percolation.