[math-fun] random walks: self-avoiding but with max self-cuddle

imagine a self-avoiding 3D walk on a diamond (tetrahedral) net, where randomness is minimised by choosing among non-occupied sites, the one(s) with maximum number of neighbours. In case of zero neighbours, explore one step further ahead until one or more sites with neighbours is found. This reduces the number of random choices between 'equivalent' continuations. Q: how far does the randomness (entropy per step) get reduced? Experiment gives about 50% reduction vs non-self-avoiding reference. Anyone seen this before? On the physics side, I can imagine processes of polymerisation where the newly formed polymer strand coils upon itself (plastics, proteins,..) Q: how far is this away from space-filling? W.