(a) Fifty simulated trials of the representation of a single memorandum, x̂I, corrupted by a static noise term representing sensory and motor noise (η1) and time-dependent noise (increasing variance corresponding to decreasing memory precision) modeled as Brownian diffusion. At time t, the report for one item, rt,1, is the location of the particle. (b) Linear accumulation of noise (variance) for single or multiple Perceived items (colors, as indicated) or Computed mean values using two different strategies (solid vs. dashed black lines, as indicated). Memory representations of N=1, 2, or 5 items have initial, additive error ηN and diffuse over time with diffusion constant σN2; thus, variance at time t=ηN+t*σN2. For the Average-then-Diffuse (AtD) model, the average is calculated immediately and stored as a single value. Thus, the diffusion constant of a Computed mean of N items is the same as for one item (σMN2=σ12; parallel purple and black lines), although η1 and ηMN may not be equal. For the Diffuse-then-Average (DtA) model, all items are stored until the probe time. Thus, the effective σMN2 is 1/Nth of σN2. (c) Relationship between A and log differences of diffusion constants for various set sizes and models. σ12 is independent from A and equal to σMN2 under AtD. σN2 is linear with A in log space with respect to (σ12) because log(σN2)–log(σ12)=A*log(N). σMN2 is linear with A. DC=Diffusion Constant. (d) Accumulation of noise for Perceived items presented sequentially. When the new (Late) point is added at time T/2, the diffusion constant for previously presented items (Early) changes slightly because of the increased load. Early and Late items for set size N have encoding noise ηNE and ηNL, respectively, represented by η(E/L). The ‘effective Early’ trace shows the net gain in variance over time that would be expected when sampling the error only at a single time T, as we did. (e) Accumulation of noise for Computed items in the Sequential condition for both models. The encoding noise for the mean of N items is represented by ηMNSeq. At time=T/2, the final point is averaged, causing a change in the diffusion constant. The ‘effective’ lines represent the measured change in variance over time one would measure when recording only at T. Here N=5, A=0.5.