construct oppairs → signalimport fullseye as fs; fs.ledger.neighbour_index_gaps(points, k=6, chunk=65536) (実装を直接呼ぶなら import mathops; mathops.neighbour_index_gaps(points, k=6, chunk=65536)、台帳から引くなら 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.
Equal-distance neighbours retain the spatial tree query’s native index order; chunking does not sort or otherwise change that tie rule.
HALCON: no operator.
mathops の全 op は入力を検証してから計算する(黙って通さない):
ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。ValueError(件数を明示して拒否 — 結果全体に伝播するため)。ValueError。reshape を明示する)。stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。py -3.11 examples/poc_theorems_as_pictures.pysignal を入力に取れる)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. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.