direction op• Data kinds: matrix × table → matrix
• Call: import fullseye as fs; fs.ledger.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean') (to call the implementation directly, import flyvision; flyvision.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean'); from the registry, opsflyvision.get("fly_t4t5_field"))
Direction-selective response over the whole eye, in the six hexagonal directions.
T4 (ON) and T5 (OFF) are the first direction-selective cells in the fly, and two mechanisms make them so: *preferred-direction enhancement*, which is the Hassenstein-Reichardt multiplication, and *null-direction suppression*, which is the Barlow-Levick division. Haag et al. measured both in one cell and wrote them as three arms reading three adjacent columns — an enhancing arm E one column *before* the centre, the direct arm D, and a suppressing arm S one column *after* it::
R = (dc + k_e * LP[E]) * (dc + k_d * D) / (dc + k_s * LP[S])
with first-order low-passes of time constant tau_s on E and S. This op runs that, or either mechanism alone, at every ommatidium and in all six lattice directions at once.
movie: (T, n) one polarity channel — the ON or the OFF half of fly_onoff_split, not both. lattice: a fly_hex_lattice result (a fly_eye_merge result is refused: its coordinates repeat, so a neighbour would be looked up in the wrong patch).
dt_s: sample interval, seconds.
model: one of four, the first three sharing the same resting value dc so that their responses are directly comparable —
• "three_arm" — the whole model above (Haag et al., *eLife* 5:e17421, 2016);
• "enhance" — the numerator alone, (dc + k_e LP[E])(dc + k_d D)/dc: preferred-direction *enhancement*, the Hassenstein-Reichardt multiplication with no veto;
• "suppress" — the denominator alone, dc (dc + k_d D)/(dc + k_s LP[S]): null-direction *suppression*, the Barlow-Levick division with no enhancement (Barlow & Levick, *J. Physiol.* 178:477, 1965);
• "hr" — the classical opponent correlator LP[E]*D - E*LP[D] with its own time constant *tau_hr_s*, which is antisymmetric by construction and so is direction-selective without either of the two mechanisms above (Hassenstein & Reichardt, *Z. Naturforsch.* 11b:513, 1956). It is fly_emd_response run over the lattice instead of a pair.
tau_s / k_e / k_d / k_s / dc: the three-arm parameters. The defaults are the paper's (tau = 250 ms, k = 5/5/10, DC = 1.0). tau_hr_s: the correlator time constant, used by model="hr" only.
reduce: how the time course becomes one number per direction — "mean" (the wide-field integration a tangential cell performs), "last" (the value at the final sample, which is how a transient is read at a chosen instant) or "max".
Returns a (6, n) float64 matrix: row *k* is the response to motion in hexagonal direction *k* (counter-clockwise from +azimuth, see HEX_STEPS), averaged over time, with the model's resting value subtracted so that no stimulus reads exactly 0. It is the (k, n) shape fly_hs_readout and fly_flow_from_directions take.
Ommatidia at the rim, which have no neighbour on one side, read exactly 0 in that direction: a detector missing an arm has no motion to report, and inventing one at the edge would put a ring of false flow around every eye.
Ground truth, and it is the paper's claim written as algebra: because the three arms multiply, the direction selectivity of the whole model is the product of the selectivities of its two halves. For any stimulus and any pair of opposite directions,
ratio("three_arm") == ratio("enhance") * ratio("suppress")
exactly, where ratio = R_preferred / R_null taken on R + dc. Two columns lit in turn, a step of amplitude 1 held for tau, with the paper's constants, give R + dc = (dc + k_e(1-1/e))(dc + k_d)/dc = 24.96 preferred and dc(dc + k_d)/(dc + k_s(1-1/e)) = 0.820 null: 4.16 from enhancement, 7.32 from suppression, 30.46 together. The tests measure all three and the identity between them.
Raises ValueError: a non-2-D / too-short / non-finite *movie*, a column count that is not the lattice's ommatidium count, a non-positive *dt_s* / *tau_s* / *tau_hr_s* / *dc*, a negative gain, an unknown *model*, and any malformed *lattice*.
• 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_fly_optomotor_steering — py -3.11 examples/poc_fly_optomotor_steering.py
matrix as input)fly_lamina_filter · fly_onoff_split · fly_flow_from_directions · fly_egomotion_from_flow · fly_hs_readout
direction)*Provenance: flyvision.py — FLYVISION 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.