Table 2.

The exponents describing SAWs embedded in a Sierpinski carpet (2D) and Sierpinski sponge (3D) of fractal dimensions, $d_{\mathrm{f}}\simeq 1.89278$ and $d_{\mathrm{f}}\simeq 2.872683$, respectively. The values of the exponents are from exact enumeration results [348] except for $g_1$, which have been taken from the MC simulation results based on the reptation algorithm [344]. The values for $\mu$ can be estimated quite accurately using the relation, $\mu =(d_{\mathrm{f}}/d)\mu \left(d\right)$ [348], where $\mu \left(d\right)$ is the coordination number of the regular lattice. This relation yields, 2.50(2) in $d=2$ and 4.26(2) in $d=3$, which are in very good agreement with the measured values.

	2D	3D
$d_{\mathrm{f}}$	$ln8/ln3$	$ln20/ln3$
$\nu$	0.75(5)	0.58(3)
$\gamma$	1.23(4)	1.36(3)
$\mu$	2.515(15)	4.26(2)
$g_1$	0.52(5)	0.33(5)
$g_2$	1.41(8)	0.10(5)
$\delta$	4.00(30)	2.65(50)