Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Year: 2025
Type: preprint
Abstract: Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for fractal graphs, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite and discrete. These results complete the foundational theory of Edge IGS by filling the gap left by the primitive case studied in [1, 2].
Source: arXiv (Cornell University)
Authors: Li, Nero Ziyu, Hu, Frank Xin, Britz, Thomas
Institutions: University of Oxford, Imperial College London, UNSW Sydney
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966559448
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