Scale Dependent Dimension in the Forest Fire Model

We propose a novel geometric form for the spatial distribution of energy dissipation that can be interpreted as a continuously varying fractal dimension from the smallest ``Kolmogorov length'' to the length scale of the largest coherent state, $l=\xi$. We show this scaling behaviour occurs in the the forest-fire-model, where the dimension of the fires varies continuously from zero to three. We speculate that this scaling form might be applicable to the spatial distribution of luminous matter in the universe, and for the dissipative field in fully developed turbulence.