  The anomalous mean square fluctuations are shown to arise naturally from the
ordinary diffusion equation interpreted scale invariantly in a formalism
endowing real numbers with a nonarchimedean multiplicative structure. A
variable $t$ approaching 0 linearly in the ordinary analysis is shown to enjoy
instead a sublinear $t\log t^{-1}$ flow in the presence of this scale invariant
structure. Diffusion on an ultrametric Cantor set is also generically
subdiffusive with the above sublinear mean square deviation. The present study
seems to offer a new interpretation of a possible emergence of complex patterns
from an apparently simple system.
