Fig. 2: Position-dependent rotational dynamics: sampling a checkerboard pattern with a sensorial delay.

a (top) Block diagram illustrating the feedback loop enforced both in experiments and simulations to achieve space-time modulations of the rotational dynamics. The feedback function that couples D_R with the particle’s position r(t) consists of four blocks in series: sampling, delay, zero-order hold (ZOH), and D_R  = f(r). a (bottom) Schematic representation of how r(t) is sampled at discrete time points t = nτ (corresponding to r[n]) and reconstructed via a ZOH model (r^*(t)) after a delay of τ, i.e., using the position r[n-1] as input. b Schematic of an ABP moving over a checkerboard pattern of rotational diffusivity. c–d Side-by-side comparison of experimental (black) and simulated (red) trajectories of ABPs with D_R varying according to the checkerboard pattern. (v = 3.5 μm s⁻¹, L = 32 μm, \({D}_{{\rm{R}}}^{{\rm{H}}}\) = 10 rad² s⁻¹, \({D}_{{\rm{R}}}^{{\rm{L}}}=0.01\) rad² s⁻¹, and τ = 0.4 s).