Self-Avoiding Walk | Basics and Probability

An overview of self-avoiding walks and their probabilities.
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About the probability computation: you are actually computing the probability that a simple random walk for n steps conditioned to not hit it's past for n steps produces that particular self avoiding wallk. This Is actually a different model from the usual self avoiding walk model which amounts to uniformly picking a self avoiding walk from all self avoiding walks of length n. The latter is actually very hard to understand and is one of the biggest open problems in statistical physics.

Hi! Can You please point in the direction of generating a self-avoiding, continuous(in a loop) broken line path that fills random areas as dense as possible and has limitation max and min length for the segments and the minimums angle(30deg for example) for corners? Thank You!