construct op• データ種: pairs → signal
• 呼び出し: import fullseye as fs; fs.ledger.neighbour_index_gaps(points, k=6) (実装を直接呼ぶなら import mathops; mathops.neighbour_index_gaps(points, k=6)、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.
Parameters
----------
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.
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):
• **complex 入力は 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。
• **masked array(masked 要素あり)は 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。
• **NaN/Inf は全入力で ValueError**(件数を明示して拒否 — 結果全体に伝播するため)。
• 形状は厳格: 1-D と 2-D を暗黙昇格・ブロードキャストしない(vector 枠に matrix、matrix 枠に vector は ValueError。reshape を明示する)。
• サイズ上限: 行列を取る op と stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
signal 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.