IRAS Rewrite Automaton

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IRAS Rewrite Automaton nilpotent kernel · nonlinear fire rule · U(K)²=0

mode: ISAR-fire

fires/step: 0

drag → inject A

I fixed-point (teal)

R asymmetry (amber)

A adjacency (purple)

S closure (green)

fire event (red flash)

ΣI

ΣR

ΣA

fires

step 0 ΣI – ΣR – ΣA – fires – Δ –

Rule modes

Switch between three nonlinear rule sets — all derived from the same kernel.

ISAR-fire rule (default)

each cell per tick:
  1. diffuse I (slow), R (fast), A (medium)
  2. A += κ·(Ī·R̄)          ← kernel row [1,1,0,0]
  3. if A > θ_fire:          ← nonlinear threshold
       fire = true
       I  -= α·I            ← rewrite consumes invariant
       R  += β·(1-R)        ← asymmetry grows
       S   = clamp(S+γ,0,1) ← closure records event
       A  -= θ_fire         ← reset (refractory)
  4. if proj ON: normalise ΣI

Firing is the discrete rewrite step: U(K) applied once. Because U(K)²=0, a fired cell cannot immediately re-fire — it must recover through diffusion first.

Parameters

I diffusion

R diffusion

A diffusion

κ feed (I·R→A)

A leak λ

fire θ

fire β (R gain)

fire α (I loss)

inject radius

speed (steps/f)

Invariant projection (ΣI conserved)

Flash fire events

ISAR-fire: Turing-like spots/waves from the kernel fire rule.
Gray-Scott: classic 2-chemical RD using U,V mapped to I,A.
Excitable: FitzHugh-Nagumo style, R = recovery variable.

Space pause · R random · S seed · 0 reset
Drag on canvas to inject A-carrier.