Complex fractal dimensions describe the hierarchical structure of diffusion-limited-aggregate clusters.

We analyze large diffusion-limited aggregates and uncover a {ital discrete} scaling invariance in their inner structure, which can be quantified by the introduction of a set of {ital complex} fractal dimensions. We provide a theoretical framework and prediction of their values based on renormalization group theory and a previous wavelet analysis. {copyright} {ital 1996 The American Physical Society.}