DOI: 10.5061/dryad.gb5mkkwxs
title: Annotated images and branch diameter data for scaling in branch thickness and the fractal aesthetics of trees

description: This is a dataset of hand-annotated branch diameters in artwork depicting
 trees, collected as part of a study designed to measure α, the diameter
 scaling exponent in fractal branching in artwork. We annotate stone window
 screen from the 16th century Sidi Saiyyed mosque, the Edo period Japanese
 painting "Cherry blossoms" by Matsumura Goshun, and 20th century
 abstract art by Gustav Klimt (from "Tree of Life") and Piet
 Mondrian ("Grey Tree" and "Blooming Apple Tree"). We
 measure the scaling exponent α by fitting branch diameter to a power law
 using logarithmic binning according to methods of Lin and Newberry (2023)
 and Newberry and Savage (2019). Included in this repository are lists of
 branch diameters and image annotations.
description: We collected branch diameters according to methods described in
 Gao and Newberry (2025). We chose works in the public
 domain that depicted trunks or large branches offering sufficient contrast
 between the largest and smallest branches to measure scaling.
 We annotate images of each work using lines in the open source
 scalable vector graphics (SVG) editing program Inkscape. We overlay line
 segments by hand perpendicular to the direction of the branch to represent
 each branch diameter.  We attempt to choose each diameter as the closest
 diameter downstream of each branch point that represents the overall
 branch diameter. That is, we measure diameter downstream of any transient
 changes in diameter such as the concave curves at Klimt's branch
 points or the leaves in Sidi Saiyyed jalis. We then load the SVG file in
 Mozilla Firefox and use JavaScript code Array.prototype.slice.call(document.getElementsByTagName("path")).map(function(a) \{ return a.getTotalLength() \}).join("\textbackslash{}n"); in the Web Developer Console to extract the branch points. We selected publicly-available images that clearly showed the works, avoiding parallax error or shadows that might obscure the branch thickness. We stopped annotating branches when small stems lead only to a single leaf or motif. That is, we do not count as branches the leaves or flowers in Sidi Saiyyed or Goshun or the Egyptian revival decorative motifs in Klimt. In Mondrian's trees, anatomical branch points are indistinct or nonexistent.  Instead, boughs are represented by long, curved brush strokes without anatomically relevant points of intersection. Therefore rather than apply the scoring rules at branch points as with the other works, we measure the diameters of each arc without regard to how the arcs intersect. We mentally decompose the tree into arcs and attempt to measure the diameter near the center of each arc. We interpret each continuous, regular dark curve as an arc, whether it is a single dark brush stroke, an absence of light brush strokes, or a discernible dark shadow underneath gray brush strokes. We roughly require each arc to curve in the same direction, so that we decompose Y- or S-shaped patterns as two or more arcs on top of each other. For consistency, we try to measure the arc near its visual ``center of gravity'', such as its midpoint, thickest point, or somewhere in between.  As the process is somewhat subjective, each author independently scored each image to control for subjectivity in assessing diameter and the presence or absence of boughs and branching, resulting in two replicates that show the extent of researcher subjectivity in interpreting the images and scoring rules. For Mondrian's "Gray Tree", we solicited a third ``blinded'' replicate from an anonymous participant 'a' who was given only an excerpt from this methods section and a figure panel from the paper. For Mondrian's "Blooming Apple Tree", only one annotator recorded branch diameters.
description: # Annotated images and branch diameter data for scaling in branch
 thickness and the fractal aesthetics of trees This is a repository of
 hand-annotated image data used in the analysis of a study of fractal
 branching of trees in art in Gao and Newberry (2025). ## Data The original
 image files are included in JPEG format. ``` gk.jpg gt.jpg mb.jpg mg.jpg
 ss1a.jpg ss1b.jpg ss2a.jpg ss2b.jpg ``` The filename without the extention
 (eg `gk` for Mondrian's "Grey Tree") is the internal ID for
 the image (`imageID`). SVG files contain overlay lines perpendicular to
 the direction of the branch representing the branch diameter downstream of
 each branch point, annotated according to methods described in Gao and
 Newberry (2025). These annotated files are named according to the scheme
 `.svg`. The annotator IDs are `m` for
 Newberry, `j` for Gao, and `a` for one anonymous participant. The `ssNb`
 image files are not annotated. ``` gtj.svg gtm.svg gta.svg gkj.svg gkm.svg
 mgj.svg mgm.svg mbm.svg ss1aj.svg ss1am.svg ss2aj.svg ss2am.svg ``` For
 each SVG, there is a corresponding file with a `.nlsv` extension for
 newline-separated values of the branch lengths, obtained by running the
 following javascript code in a web browser with the SVG file loaded. ```
 Array.prototype.slice.call(document.getElementsByTagName("path")).map(function(a){return a.getTotalLength()}).join("\n"); ``` This code generates the contents of the nlsv file as a javascript variable. The branch diameter units are arbitrary. Two special files `grove5.svg` and `grove5.tsv` contain random computer-generated trees and the corresponding branch diameters. `grove5.tsv` is a tab-separated values file with the header `alpha` indicating the value of α used to generate the tree, and `diameter` in arbitrary units. ## Reproducibility Code for reproducing results of this study is provided in the github repository [https://github.com/mnewberry/treescale](https://github.com/mnewberry/treescale). Some data files used in the study are not public domain and hence cannot be included in this repository. Those data files were obtained from Brummer et al. (2021) published by the Royal Society under the terms of the Creative Commons Attribution License and are available in the github repository as `samples/balsa.nlsv`, `samples/pinon.nlsv`, and `samples/ponderosa.nlsv`. ## References Gao, J & Newberry, M.G., (2025) Scaling in branch thickness and the fractal aesthetics of trees. PNAS Nexus. [https://doi.org/10.1093/pnasnexus/pgaf003](https://doi.org/10.1093/pnasnexus/pgaf003) Lin, Q. & Newerry, M.G., (2023) Seeing through noise in power laws. J. Roy. Soc. Interface, 20(205):20230310. [https://doi.org/10.1098/rsif.2023.0310](https://doi.org/10.1098/rsif.2023.0310) Newberry, M. G., & Savage, V. M. (2019) Self-similar processes follow a power law in discrete logarithmic space. Physical review letters, 122(15), 158303. [https://doi.org/10.1103/PhysRevLett.122.158303](https://doi.org/10.1103/PhysRevLett.122.158303) Brummer A.B., Lymperopoulos P., Shen J., Tekin E., Bentley L.P., Buzzard V., Gray A., Oliveras I., Enquist B.J. & Savage V.M. (2021) Branching principles of animal and plant networks identified by combining extensive data, machine learning and modelling. J. R. Soc. Interface. 18:20200624. [http://doi.org/10.1098/rsif.2020.0624](http://doi.org/10.1098/rsif.2020.0624) ## Licensing and usage authorization All data collected in this study are the original work of the authors and hereby released into the public domain. The image files were obtained from Wikimedia Commons and are faithful reproductions of works in the public domain, are therefore considered public domain according to the laws of the United States of America and are hence used here without further attribution.