construct op• Data kinds: pairs → signal
• Call: import fullseye as fs; fs.ledger.neighbour_index_gaps(points, k=6) (to call the implementation directly, import mathops; mathops.neighbour_index_gaps(points, k=6); from the registry, opsmath.get("neighbour_index_gaps"))
How far apart *in index* are a point's nearest neighbours — parastichy as a number.
In a phyllotactic pattern the visible spirals (parastichies) are not drawn by anything; they are an illusion of which florets happen to sit next to each other. This op replaces the illusion with a count: for every point, take its *k* nearest neighbours in space and record the difference of their ordering indices. The histogram of those differences is returned, index g holding how many neighbour pairs were g apart.
★Why this earns its place: with the golden angle the peaks land on Fibonacci numbers (8, 13, 21, 34, 55 ...), and with any other angle they do not. That is a statement about the arrangement which can be checked without looking at the picture — which is the whole point, because the spirals look convincing at every angle.
points : (N, 2) array
Ordered points — the order is the data here, not a convenience.
k : int >= 1
Neighbours per point (6 is the natural choice: a well-packed planar
arrangement is locally hexagonal).
Returns a signal: counts[g] = number of neighbour pairs whose index difference is g (counts[0] is always 0 — a point is not its own neighbour).
Raises ValueError: not an (N, 2) array; fewer than k + 1 points; k below 1; non-finite coordinates.
Limits: the first points of a spiral sit near the centre where the packing is degenerate, so the histogram has a low-index tail that carries no parastichy information. Compare *peaks*, not the raw tail.
HALCON: no operator.
Every mathops op validates its input before computing (nothing slips through silently):
• complex input raises ValueError — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• masked arrays with masked elements raise ValueError — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• NaN/Inf raises ValueError on every input (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• 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 canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · ifs_fractal · ifs_similarity_dimension · space_filling_curve · curve_locality
*Provenance: mathops.py — MATH 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.