Abstract
We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinskitype fractals of Hausdorff dimension 1 <d <sub>f</sub> ≤ 3 in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of the Wolff cluster and are able to establish a different scaling relation. It enables us to introduce an exponent that is associated to the surface energy of the Wolff cluster. Finally, this exponent is linked to a dynamical exponent via an inequality.