Annotated images and branch diameter data for scaling in branch thickness and the fractal aesthetics of trees

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.

Methods
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.