--- type: Paper Section title: Metabolic Scaling — Abstract description: >- Abstract and key findings of the Part II manuscript: the ecological literature misdescribes vascular branching networks as self-similar, metabolic scaling theory implies they are self-affine, and a mechanistic theory of fractal dimension is proposed from single cells to multicellular life. resource: https://tyson-swetnam.github.io/fractal-notebooks/metabolic-scaling/abstract/ tags: [paper, part-ii, metabolic-scaling, self-affinity, self-similarity] paper: title: "Fractal Patterns in Nature: Self-Affinity vs Self-Similarity" part_title: Metabolic Scaling Theory and Biological Fractals landing: https://tyson-swetnam.github.io/fractal-notebooks/metabolic-scaling/ stage: manuscript-draft authors: - name: Tyson Lee Swetnam orcid: https://orcid.org/0000-0002-6639-7181 affiliation: Institute for Computation and Data-enabled Insight, University of Arizona - name: Jon D Pelletier orcid: https://orcid.org/0000-0002-0702-2646 affiliation: Department of Geosciences, University of Arizona - name: Brian J. Enquist orcid: https://orcid.org/0000-0002-6124-7096 affiliation: Department of Ecology and Evolutionary Biology, University of Arizona citation: key: swetnam2026fractals year: 2026 publisher: GitHub url: https://github.com/tyson-swetnam/fractal-notebooks generated: by: human:tswetnam at: "2025-12-14T00:00:00Z" status: draft --- # Abstract Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License. Much of the scientific literature describes the fractal-like hierarchical branching networks of vascular organisms as 'self-similar'. Here we examine papers where fractal-like self-similarity is incorrectly described. We also link why the hierarchical branching networks in vascular organisms are 'self-affine' rather than self-similar by linking metabolic scaling theory to these structural traits. Last, we propose a mechanistic theory of fractal dimensions for single cell through multicellular life forms. In our supplemental materials, we provide empirical explanations for the fractal-like structures of single cell colonies and autotrophs including primitive algae, vascular organisms including lichens and bryophytes, and higher order terrestrial plants. We also describe how self-affinity arises in heterotrophs as related to metabolic and circulatory networks. ## Key Findings 1. **Dimensional analysis with appropriate self-affine mass dimension** shows that many reported fractal dimensions in ecology are either incorrect or inappropriately reported. 2. **A technique for testable predictions**, including a mechanistic explanation for how individual branching networks grow and fill space and how communities of organisms emerge with fractal dimensions based on MST predictions. 3. **Self-affine vs self-similar**: The distinction between these concepts has significant implications for how we measure and interpret fractal dimensions in biological systems. These results may help reveal when communities of individuals have maximized their potential to cycle energy through an ecosystem or when they have been disturbed by exogenous forces. The manuscript table of contents, the supporting notebooks and the author list are on the [Part II landing page](index.md).