complex op• Data kinds: cimage → mask
• Call: import fullseye as fs; fs.ledger.mandelbrot_interior(c) (to call the implementation directly, import mathops; mathops.mandelbrot_interior(c); from the registry, opsmath.get("mandelbrot_interior"))
Closed-form interior test for the main cardioid and the period-2 bulb.
Returns a boolean array: True where c is provably in the Mandelbrot set, because the period-1 fixed point is attracting (|1 - sqrt(1 - 4c)| < 1) or c lies in the period-2 bulb (|c + 1| < 1/4). False means "not proven by these two tests" — the smaller bulbs and the filaments are not covered, so this is a lower bound on the set, which is exactly what makes it usable as a gate: cplx_escape_time must return max_iter everywhere this is True, and no tolerance is involved.
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_complex_plane_fields — py -3.11 examples/poc_complex_plane_fields.py
mask as input)—
complex)cplx_contour_circle · cplx_poly_eval · cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski
*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.