Watch a system remember
Follow a scalar state through repeated updates. Explore how an update rate changes its response.
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Watch a state remember
Apply a sequence of inputs to one persistent number. Explore forgetting, oscillation, and unstable feedback.
s is the persistent scalar state; a controls the retained prior state; b scales the input u. The same stored state is updated at every step. For this linear recurrence, differences in initial conditions shrink when |a| < 1. This one-number demonstration is not a neural network, a trained model, or an operating Pantheon runtime.
Try this: choose a single pulse and compare a = 0.8, −0.8, and 1.2. Which settings forget an earlier state, and which amplify it?
Playback starts only when you choose Play. It pauses when this tab is hidden or the lab leaves view. Reduced-motion preferences slow the updates; Step always gives you direct control. Runs stop after 40 updates or at the display limit.
The default worked example is shown below.
Stable memory: differences in initial state shrink because |a| < 1. Press Step to apply the first input to the initial state. The constant-input fixed point is b / (1 − a) = 1; convergence to it requires |a| < 1.
| Update | Input u | Previous state | New state |
|---|---|---|---|
| 0 | Not yet applied | Initial condition | 0 |
Learn the ideas behind this lab.
Follow a worked example, practice on your own, and return to the original project sources.
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