construct op• Data kinds: none → pairs (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.space_filling_curve(kind='hilbert', order=4) (to call the implementation directly, import mathops; mathops.space_filling_curve(kind='hilbert', order=4); from the registry, opsmath.get("space_filling_curve"))
Hilbert / Moore / scan orders on a `2**order` square — a permutation, checked.
Returns the visiting order as `pairs (4**order, 2)` of integer grid
coordinates. Two scan orders are included as control groups, not as
filler: `row_major` jumps a whole row at the end of each line and
`boustrophedon` (serpentine) does not, so "consecutive points are
adjacent" separates them, and the locality measurement separates all four.
★Why this earns its place — the defining properties are integers:
• The result visits `4**order` cells, each exactly once: a
permutation, verified by sorting, not by sampling.
• For Hilbert, Moore and boustrophedon, **consecutive points are always at
L1 distance exactly 1**. Row-major is not (it jumps at every line end),
which is the control.
• Moore's curve is closed: the last point is adjacent to the first.
Hilbert's is not.
• *Locality.* For a gap of `k` in index, the mean Euclidean distance
grows like `sqrt(k)` for Hilbert and much faster for row-major. That is
why Hilbert order is used for spatial indexes, and it is measurable here
rather than asserted.
Raises `ValueError: unknown kind; order < 1`; the grid would
exceed the cap; `moore with order < 2` (it is not defined below that).
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
pairs as input)neighbour_index_gaps · curve_locality
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · ifs_similarity_dimension · 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.