Each of the N β 420 dots is a hippocampal/amygdalar neuron with a fixed excitability ei (a stand-in for CREB level β cells with more CREB are more likely to be allocated into an engram, the neuronal allocation hypothesis). This 2D build lays the same population out on a flat elliptical field instead of the 3D version's ellipsoid β a projection, not a different model: the allocation and reactivation math below is copied verbatim from the 3D engine and re-verified numerically to match. Encoding an experience drives activity:
a_i = clamp( e_i + Ξ·Β·(1 β s), 0, 1 ), Ξ· ~ U(β0.5, 0.5)
tagged_i β a_i > threshold
where s is the context-similarity slider. Low similarity injects independent noise into each encoding, so two different contexts recruit largely different cells; high similarity makes both events driven by the same underlying excitability ranking, so the same high-e cells get tagged twice β the biological source of engram overlap, measured live as the Jaccard index |Aβ©B| / |AβͺB|. The histogram panel below the field plots the raw excitability distribution with the threshold line drawn live, so you can see directly why raising the threshold shrinks both engrams while raising similarity makes the blue and red histograms converge.
Reactivation models channelrhodopsin-2 optogenetic drive: light power P sets a saturating recruitment probability Preactivate = 1 β eβ3P for cells tagged during the fear (Context B) encoding β this is exactly the ChR2 pathway used to artificially reactivate a fear engram (Liu, Ramirez, Tonegawa 2012 β implanting a false fear memory by light-reactivating cells tagged during shock, in an animal that is physically in a neutral box). The resulting freezing readout:
freeze % = 5 + 15Β·overlap + 70Β·PΒ·(1 β e^(β3P))
so freezing rises both from natural generalisation (overlap between the two ensembles) and from direct optogenetic reactivation of the shock-tagged cells β the two routes real engram studies use to distinguish genuine recall from artificially implanted fear.