Scale decomposition of unstable growing fronts

We present results obtained from the wavelet transform of unstable growing fronts. The linear growth equation is transformed using the Hermitian wavelets obtained from recursive shifts and changes in the Gaussian filters. We explore the evolution of the instability at different scales, and at different locations (in the direct space) in the wavelet domain, using a numerical growth model and the experimental example of chemically etched silicon. Wavelet formalism may have an advantage over Fourier methods in the sense that one can track the instability in the location (direct space) and at different scales simultaneously. It also provides a quantitative tool for the characterization of the growing fronts through its concise scale discrimination.