Average number of steps before termination: | 70.7598 | +-0.001 |

Average number of failed attempts: | 45.0295 | +-0.001 |

Number of walks in simulation | 1.2*10^{10} |

Examples for walks with the maximum number of constrained steps

Conjecture: A n-step 2D STW has never more than n-floor(sqrt(4*n+1))-2 steps

with only two choices for the possible next direction.

n-floor(sqrt(4*n+1) is Sequence A076874 in Sloane's OEIS.

5 Unconstrained and 7 maximally 2-constrained walks of length 10

Manhattan Distance Start-End for n-step Self-Avoiding Walks

Asymptotic Behavior of Mean Square Displacement

Asymptotic Behavior of Mean Manhattan Displacement

End-to-End Euclidean Distance Distribution of all 25-Step Walks

Count self-trapping walks up to length 23

Enumeration of all short self-trapping walks

7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

Distribution of end point distance

Average Euclidean and squared end point distance

Average Manhattan end point distance

Comparison of average Euclidean and Manhattan displacements

Unsolved Problem: Is there an asymptotic
value for the difference between the average
displacement of all self-avoiding n-step walks and the subset of self-trapping n-step
walks for large n.

See figure: Manhattan displacement difference SAW-STW.

Fortran program for distance counting