construct op• Data kinds: none → measurement (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.ifs_similarity_dimension(preset='sierpinski', maps=None, tol=1e-13) (to call the implementation directly, import mathops; mathops.ifs_similarity_dimension(preset='sierpinski', maps=None, tol=1e-13); from the registry, opsmath.get("ifs_similarity_dimension"))
Moran's equation `sum(r_i**d) = 1 solved for d` — from the maps alone.
The similarity dimension of a self-similar set, computed before anything
is drawn. Valid when the pieces overlap only on a set of measure zero (the
open set condition); affine maps that are not similarities (the fern) have
no single ratio, so this raises rather than returning a number that looks
right (measured: the fern's four maps have singular-value ratios from 0.16
to 0.85, so no `r_i` exists).
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
measurement as input)—
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · space_filling_curve · 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.