Monte Carlo simulations have been performed on tethered networks possessing the connectivity of a b=2 Sierpinski gasket, both with and without self-avoidance. For networks without self-avoidance, the simulations are found to be in reasonable agreement with the theoretical prediction, nu0~=0.3685, and independent of the embedding dimension d. For networks with self-avoidance, the simulations give
... [Show full abstract] clear evidence for crumpling. The measured value for nu is in good agreement with the Flory theory and, to a lesser extent, the first-order ε expansion of an appropriately generalized Edwards model. The upper critical dimension, dUC, above which self-avoidance is irrelevant, is found to lie in the range 8