Spatiotemporal fluctuations in growth phenomena: Dynamical phases and 1/fnoise

We find that the dynamics of growth phenomena exhibits the feature that growing sites are naturally partitioned into two ‘‘dynamical phases,’’ an extinct phase (the sites at which no further growth occurs, in a statistical sense) and a surviving phase (where growth occurs at some later time). As examples, we treat two common growth phenomena, invasion percolation and diffusion-limited aggregation. For both examples, we find ‘‘subclusters’’ which exhibit spatio-temporal fluctuations that are scale invariant. We find a 1/${\mathit{f}}^{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ power spectrum for both models. Also, we identify an order parameter and find an associated exponent β.