Abstract
“Normal” and indefinitely-growing (IG) self-avoiding walks (SAWs) are exactly enumerated on several deterministic fractals (the Manderbrot-Given curve with and without dangling bonds, and the 3-simplex). On then th fractal generation, of linear sizeL, the average number of steps behaves asymptotically as 〈N〉=ALDsaw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and “normal” SAWs have the same fractal dimensionDsaw. However, they have different amplitudes (A) and correction terms (B).
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