  Drawing on analogies with the commutative case, the Wilsonian picture of
renormalization is developed for noncommutative scalar field theory. The
dimensionful noncommutativity parameter, theta, induces several new features.
Fixed-points are replaced by `floating-points' (actions which are scale
independent only up to appearances of theta written in cutoff units).
Furthermore, it is found that one must use correctly normalized operators, with
respect to a new scalar product, to define the right notion of relevance and
irrelevance.
  In this framework it is straightforward and intuitive to reproduce the
classification of operators found by Grosse & Wulkenhaar, around the Gaussian
floating-point. The one-loop beta-function of their model is computed directly
within the exact renormalization group, reproducing the previous result that it
vanishes in the self-dual theory, in the limit of large cutoff. With the link
between this methodology and earlier results made, it is discussed how the
vanishing of the beta-function to all loops, as found by Disertori et al.,
should be interpreted in a Wilsonian framework.
