dynsys oppoints → measurementimport fullseye as fs; fs.ledger.dynsys_correlation_dimension(points, n_radii=24, r_lo=None, r_hi=None, max_points=4000, seed=0) (実装を直接呼ぶなら import mathops; mathops.dynsys_correlation_dimension(points, n_radii=24, r_lo=None, r_hi=None, max_points=4000, seed=0)、台帳から引くなら opsmath.get("dynsys_correlation_dimension"))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).
Pair distances use condensed storage and are sorted once; all strict
distance < radius counts then come from one binary-search operation.
★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.
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_what_a_picture_cannot_check.pymeasurement を入力に取れる)—
dynsys)ode_flow_states · ode_vector_field_grid · dynsys_poincare_section · dynsys_lyapunov_spectrum · dynsys_bifurcation_map
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.