The version referred to in
S. R. Finch, Mathematical Constants,
Cambridge Univ. Press, 2003:
A note on the height of binary search trees,
random sequential bisection,
and successive approximation for differential equation
with moving singularity, 1998,
is old,
and considerably a lot has been added in the above later versions.
M. T. Barlow, K. Hattori, T. Hattori, H. Watanabe,
Weak homogenization of anisotropic diffusion on pre-Sierpinski
carpet,
Communications in Mathematical Physics 188 (1997) 1-28.