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A procedure for virtually memory-free Monte-Carlo simulation of the self-avoiding random walk (SAW) in a two-dimensional network and in a simple cubic lattice has been developed. It is highly efficient in yielding values of the intrachain meansquare end-to-end distance &lt;r2 n &gt; for chains up to n = 1000 and n = 400 steps, for the two and three-dimensional cases respectively. The number  N  of walks per each chain of  n  steps involved n = 500 to N = 3000.Accessing a medium-sized computer via a portable terminal, it was possible to obtain values for  n  up to 21, with N up to 1000, in minutes, and to obtain values for  n  up to 400 and 1000 with N up to 300 in approximately an hour of computing time.The principal finding is that for &lt;r2 n &gt; = anγ , the value of the exponent remains stable at approximately 6/5, consistent with the results of prior work involving complete enumeration for  n  up to 16 and  n  up to 10 in the two-dimensional and three-dimensional cases. No comparative data are available for higher levels of  n  because of the time constraints of memory-dependent computer programs.

A Monte Carlo approach for the solution of the simple quadratic and cubic self-avoiding random walk