typed op• Data kinds: points → feature
• Call: fullseye.apply(img, "tb_dynsys_correlation_dimension", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
Sweeping knob a (0.1 / 0.5 / 0.9, the other knob at its default):
▸ tb_dynsys_correlation_dimension: knob a sweep (docs site)
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_dynsys_correlation_dimension: stages (docs site)
Grassberger-Procaccia correlation dimension — the slope of `log C(r)`.
`C(r) is the fraction of point pairs closer than r`; for a self-similar
set it grows like `r**D`, and *D* is read off the straight part of the
log-log plot (fitted on the middle 60 % of the radii, where the curve is free
of the small-`r noise floor and the large-r` saturation).
★Why this earns its place: unlike box counting it needs no grid, and its
answers are known for simple sets — a circle gives 1, a filled square
2, a Cantor set `log2/log3 = 0.6309`. It measures a different quantity
from the existing `fractal_dimension` (box counting), so the two are an
independent pair rather than two names for one number.
Returns a `measurement`: the fitted dimension.
Raises `ValueError`: fewer than 32 points; not a 2-D array; non-finite
input; a degenerate cloud (every point identical); a radius range that leaves
no pairs.
Limits: sub-sampled to *max_points* (pairs grow quadratically). ★The
dominant error is not the sub-sampling but the radius window: the
default range is the 1st-25th percentile of pair distances, and on a *bounded*
set its upper end runs into the boundary, where `C(r)` saturates and flattens
the slope. Measured on a unit square (true D = 2): 1.879 with the default
window and 1.873 / 1.879 / 1.871 at 400 / 1,500 / 3,000 points —— more points
do not help; narrowing the window to `r_lo=0.01, r_hi=0.1` gives 1.947
and `0.002 / 0.05` gives 2.050. Pass *r_lo* / *r_hi* explicitly when the
answer matters, and report the window with the number.
Typed bridge of the math op `dynsys_correlation_dimension into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives n_radii (default 24); b` is unused.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_points 0.50 0.50 tb_dynsys_correlation_dimension 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op dynsys_correlation_dimension. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• poc_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
feature as input)typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.