a fMRI patterns formed by concatenating responses across voxels for each of two experimental conditions—here, visual gratings oriented either 45° or 90° from the horizontal. The strength of the signal component distinguishing the brain responses associated with these two gratings can be quantified as the Euclidean distance between these two spatially distributed brain response patterns, treated as vectors, and denoted here as \(\vec v\) and \(\vec w\). b Simulation results: signal strength as a function of tuning bandwidth and granularity. In the class of models implemented by Alink et al., the tuning bandwidth of feature-tuned neural populations has been parametrized by Gaussian distributions. The preferred orientation of each neural population is described by μTuning, while σTuning describes how tightly tuned each population is about its preferred orientation. In turn, the level of granularity of simulated fMRI data has been controlled by a positive integer (G) specifying the number of similarly tuned neural clusters, here referred to as granules, assumed to be sampled by each voxel13. The 3D surface shown to the right under the label “Simulation results” clearly demonstrates that granularity (x-axis), as well as tuning width (y-axis), influence the strength of simulated fMRI patterns. For each admissible parameter combination of G and σTuning the z-axis indicates the average strength (across 25 randomly seeded simulations) of the signal distinguishing the fMRI response patterns denoted by \(\vec v\) and \(\vec w\). The full range of simulated granularity levels is [1, 512] (2n, with n = 0, 1, …, 9 granules per voxel). A dramatic effect of granularity on signal strength can be noted along the x-axis. If granularity were irrelevant, the observed monotonically decreasing curve would be instead a flat line. Given that pairwise correlations are known to be determined by noise amplitude as well as signal strength, this simulation demonstrates that the validity of inferences regarding neural coding based on fMRI–pattern correlations depend on granularity assumptions as well as noise parameters.