Different types of self-avoiding walks on deterministic fractals

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=AL^D_saw+B. In contrast to SAWs on regular lattices, on these factals IGSAWs and normal SAWs have the same fractal dimensionD_saw. However, they have different amplitudes (A) and correction terms (B).