Fractal dimension and grand Universality of critical phenomena

Conformation of branched random fractals formed in equilibrium processes is discussed using a Flory-type theory. Within this approach we find only three distinct types or classes of random fractals. We call these theextended, thecompensated, and thecollapsed states. In particular, the critical clusters in thermal phase transitions are found to be of the compensated type and have approximately the same value of the fractal dimension. The Flory theory predicts the upper critical dimension for these clusters to be 6 instead of 4. This result and the apparent grand universality of the fractal geometry of the clusters in critical phenomena are discussed.