Global structure and finite-size effects in the f(alpha) of diffusion-limited aggregates

The multifractal spectrum f(alpha) characterizing the scaling properties of the growth probability on the boundary of radial diffusion-limited aggregates is known to exhibit strong finite size effects. We demonstrate that there exists a correlation between these finite size effects and those present in measurements of the angular width of the fjords which lie between the principal cluster arms. We subsequently conclude that it is the evolution in the global structure of the clusters which is responsible for the slow convergence in f(alpha) and discuss how this global structure induces a phase transition in f(alpha).