  Drawing analogies with block spin techniques used to study continuum limits
in critical phenomena, we attempt to block up D-branes by averaging over near
neighbour elements of their (in general noncommuting) matrix coordinates, i.e.\
in a low energy description. We show that various D-brane (noncommutative)
geometries arising in string theory appear to behave sensibly under blocking
up, given certain key assumptions in particular involving gauge invariance. In
particular, the (gauge-fixed) noncommutative plane, fuzzy sphere and torus
exhibit a self-similar structure under blocking up, if some ``counterterm''
matrices are added to the resulting block-algebras. Applying these techniques
to matrix representations of more general D-brane configurations, we find that
blocking up averages over far-off-diagonal matrix elements and brings them in
towards the diagonal, so that the matrices become ``less off-diagonal'' under
this process. We describe heuristic scaling relations for the matrix elements
under this process. Further, we show that blocking up does not appear to
exhibit any ``chaotic'' behaviour, suggesting that there is sensible physics
underlying such a matrix coarse-graining. We also discuss briefly
interrelations of these ideas with B-fields and noncommutativity.
