A declared history.
A fixed sequence of inputs updates a memory value and produces a bounded response. The record contains every step.
The public observatory
A small model.
A revealing difference.
Explore how a history can shape a response. Run the same conditions again, then change one input and follow the divergence.
Exhibit 01 / History-dependent dynamics
Illustrative model · Local onlyThe continuity experiment
Baseline responseCounterfactual response
Fixed seed / 42 · 96 steps
Ready. Run the model to draw a complete trajectory. No live system is connected.
This exhibit runs only in your browser. It is a small mathematical illustration created for this website—not the Psyche Lab engine, Luna’s internal state, a published experiment, or a consciousness test.
The same conditions.
Replay repeats the declared inputs. The exhibit compares the complete generated record rather than trusting a similar-looking line.
A different future.
An input pulse changes a short interval. Memory can carry part of its influence beyond the pulse itself.
Under the exhibit
Simple enough
to inspect.
The purpose is to understand an experimental distinction, not to simulate a whole mind.
The memory state begins at zero. At each step, it combines its previous value with a seeded input. The response depends on both the present input and the updated memory.
m[t+1] = r · m[t] + (1 − r) · u[t] y[t] = tanh(1.9 · m[t+1] + 0.55 · u[t]) Intervention: +0.65 to u[t], steps 32–39 r: selected retention, from 0.00 to 0.95
A longer tail after the intervention is a consequence of this equation. It is not evidence of a felt experience, a learned preference, or a psychological trait.
Exported records include inputs, both trajectories, the seed, retention, intervention window, and an explicit illustrative-model label. Changing a control marks the prior run as stale until you run again.