  The forest fire model is a reaction-diffusion model where energy, in the form
of trees, is injected uniformly, and burned (dissipated) locally. We show that
the spatial distribution of fires forms a novel geometric structure where the
fractal dimension varies continuously with the length scale. In the three
dimensional model, the dimensions varies from zero to three, proportional with
$log(l)$, as the length scale increases from $l \sim 1$ to a correlation length
$l=\xi$. Beyond the correlation length, which diverges with the growth rate $p$
as ${\xi} \propto p^{-2/3}$, the distribution becomes homogeneous. We suggest
that this picture applies to the ``intermediate range'' of turbulence where it
provides a natural interpretation of the extended scaling that has been
observed at small length scales. Unexpectedly, it might also be applicable to
the spatial distribution of luminous matter in the universe. In the
two-dimensional version, the dimension increases to D=1 at a length scale $l
\sim 1/p$, where there is a cross-over to homogeneity, i. e. a jump from D=1 to
D=2.
