dynsys 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.dynsys_bifurcation_map(kind='logistic', r_lo=2.5, r_hi=4.0, n_r=800, burn_in=300, keep=100, x0=0.5) (to call the implementation directly, import mathops; mathops.dynsys_bifurcation_map(kind='logistic', r_lo=2.5, r_hi=4.0, n_r=800, burn_in=300, keep=100, x0=0.5); from the registry, opsmath.get("dynsys_bifurcation_map"))
The orbit diagram of a 1-D map — period doubling, as points you can count.
For each parameter value the map is iterated `burn_in` times (discarded) and
the next `keep states are returned. logistic is r x (1 - x)`,
`sine is r sin(pi x), tent is r min(x, 1-x) * 2`.
★Why this earns its place: the first period-doubling values are known
exactly for the logistic map — `r = 3 and r = 1 + sqrt 6 = 3.449489...`
— and the ratio of successive intervals tends to Feigenbaum's constant
`4.669201..., which is universal. Counting distinct states per r` turns
the picture into integers (1, 2, 4, 8, ...) that can be checked.
Returns a `pairs array of (r, x)`.
Raises `ValueError: unknown map; r_lo >= r_hi`; non-positive counts;
a grid over the cap; `x0` outside the unit interval.
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_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
pairs as input)neighbour_index_gaps · curve_locality
dynsys)ode_flow_states · ode_vector_field_grid · dynsys_poincare_section · dynsys_lyapunov_spectrum · dynsys_correlation_dimension
*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.