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PID-Regulated Cellular Automaton

A cellular automaton whose update rule is a per-cell PID controller: each cell measures its active-neighbor count against a target and computes proportional, integral, and derivative terms to decide its next state. The result is a rule family with local memory (integral windup), local anticipation (derivative), and tunable dynamical regimes — under-damped ripples, critically-damped blobs, over-damped glassy creep — all from the same control-theoretic mechanism.

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PID-Regulated Cellular Automaton

Reference implementation of the specification in idea.md: a discrete-state, discrete-time cellular automaton whose update rule is a per-cell PID controller regulating the cell's active-neighbour count N_t(c) toward a target T.

Running

ES modules require an HTTP origin (they will not load from file://):

python3 -m http.server 8080
# then open http://localhost:8080/index.html

No build step, bundler, or backend is required.

Module map

File	Role
`js/config.js`	Parameter schema, defaults, validation, JSON/hash serialisation, change notification
`js/grid.js`	State + controller-state buffers, neighbour enumeration, boundary conditions, initial conditions, seeded PRNG
`js/controller.js`	Pure PID computation: `(e_(t-1), I_(t-1), e_t, gains) -> (P, I, D, u)` with anti-windup clamping
`js/stateExpression.js`	Pluggable `u_t -> state` strategies: threshold, quantisation, semantic, probabilistic
`js/simulation.js`	One synchronous timestep per call, double buffering, playback scheduling, statistics
`js/renderer.js`	Canvas drawing of states plus optional `u_t` / `I_t` / `e_t` heat overlay
`js/ui.js`	Schema-driven control panel, playback buttons, grid painting, presets, export/import
`js/presets.js`	Named configurations for the behaviour classes in §10 of the spec
`js/main.js`	Wiring + frame scheduler

Update semantics

Each step is a pure function of (states_t, prevError_t, integral_t, config). All cells read a frozen snapshot; results are written to shadow buffers and swapped atomically (Grid.commit()), so runs are deterministic for a given seed and configuration — except in probabilistic expression mode, whose randomness is itself seeded by config.seed.

Controls

Space play/pause, S single step, R reset, C clear.
Click/drag the grid to paint cells; shift-drag or right-drag erases.
Every parameter is live-editable; grid-size changes reallocate and reset.
Copy share link encodes the non-default parameters into the URL hash.
Export/Import JSON round-trips the full configuration for presets.

Extending

New expression regime: add an entry to STRATEGIES in stateExpression.js and to the expression enum options in config.js.
New topology: extend neighborOffsets / countActiveNeighbors in grid.js.
Spatial gain fields: replace the scalar reads of cfg.kp/ki/kd inside simulation.step() with per-cell buffers; controller.js needs no change.