Uncovering a multiplicative process in one-dimensional cuts of diffusion-limited aggregates
A. Arnéodo, Françoise Argoul, Jean–François Muzy, M. Tabard, Emmanuel Bacry · The Journal of Difference Equations and Applications · 1995
Using a tree-matching algorithm specially devoted to solving the inverse fractal problem, we explore the wavelet transform modulus maxima skeletons of azimuthal Cantor sets obtained by intersecting large mass diffusion-limited aggregates with a circle. This study reveals the pertinence of a "cookie-cutter" piece-wise linear 1D map to account for the presence of a statistically predominant Fibonacci structural ordering. Two sources of randomness are identified: (i) the first one results from some symmetry in the Fibonacci multiplicative process itself: (ii) the second one appears as intrinsic noise in the reconstructed 1D map and is related to structural defects in the Fibonacci fractal hierarchy.