11 Oct
2013
11 Oct
'13
12:33 p.m.
Suppose we take one map-of-France (MOF) -- by which I mean just the boundary, of Hausdorff dimension equal to log_7(9), and fill it in with 7 copies each shrunk by a linear factor of sqrt(7). And then for each of those we do the same thing . . . ad infinitum. Is there a reasonable way to assign a Hausdorff dimension to the union of all these stages? Hmm -- I suppose it's still d = log_7(9), but with the Hausdorff d-dimensional content = oo. --Dan