Information Horizon Lab

Steering a chemically fuelled Janus micromotor on aged measurements. After When Information Expires in Self-Powered Matter (A. A. Solovev, Radcliffe proposal).

Simulation · 2D active Brownian model · not experimental data

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Bench

SIMULATION

t = 0.0 s

Space play/pause · → step one loop stage · 1–6 chapters

Position age Δt_x age of the position estimate used to aim at the target

Heading age Δt_θ age of the heading estimate used to decide the turn

Measurement noise camera noise; calibrated heading s.d. σ_θ

Efference copy (credit own commanded turns) PRESETS

Survival and restricted mean first-passage time

Fraction not yet at the target, S(t). R = area under S(t) up to T_h = 60 s, i.e. the mean of min(T, T_h).

Feedback, R_FYoked replay, R_Y

Navigational value of information, G = 1 − R_F/R_Y

Reference sweep from this page's model; point = live trials at the current setting.

Repeated trials

Estimate of G and its 95% interval as paired trials accumulate (feedback trial i → yoked trial i).

Model parameters

τ_R = 2.58 s: in-plane orientational memory time; heading diffusion D_θ = 1/τ_R
v = 10 µm s⁻¹: self-propulsion speed; L/v = 1.16 τ_R
L = 30 µm, r_c = 5 µm: start separation and capture radius of the virtual target
T_h = 60 s: observation window (23 τ_R); trials not captured are censored at T_h
0.1 s, 2°: control tick (= frame interval) and maximum commanded turn per tick
D_t = 0.29 µm² s⁻¹: assumed; Stokes–Einstein value for a 1.5 µm sphere consistent with τ_R
0.16 µm px⁻¹: assumed camera sampling; estimator precision calibrated by Monte Carlo
σ_θ = 10° (default): heading-estimate s.d.; not specified in the proposal, adjustable from the pixel floor (≈5°) to 35°

Assumptions and limits

Planar motion and in-plane rotation; magnetic moment parallel to the propulsion axis.
Uniform field: torque only, no gradient force; turn delivered by a field pulse perpendicular to the freshest heading estimate.
Decision rule: turn by up to 2° per tick toward the bearing of the target computed from the remembered position and heading.
Yoked replay: the same commanded-turn sequence applied to a particle with the same start separation and an independent heading.
Live batch trials use Gaussian estimation errors with the calibrated σ_θ, σ_xy; no loop latency beyond the set ages; no estimator lag.
Outputs measure the functional value of state information, not extracted work.

Parameters follow Fig. 1 of the proposal (two-dimensional active Brownian particle model). The proposal does not state the model's measurement noise; this page defaults to σ_θ = 10°, inside the ≤ 20° tracking specification of Aim 1. At that setting this page's reference sweep gives G(0) = 0.45 ± 0.01 and half-decays of 0.46 τ_R (heading aged), 0.59 τ_R (heading, efference copy), 1.26 τ_R (position aged) and 0.43 τ_R (both aged). The proposal reports G(0) ≈ 0.49 and 0.47, 0.59, 1.24 and 0.41 τ_R. Across σ_θ = 5–30° the heading half-decay stays within 0.46–0.49 τ_R, while G(0) falls from 0.45 to 0.35.