Emergence from rules

October 15, 2025

Three systems.
Three rule sets.
No blueprint.
No hierarchy.

Rule_1 Diffusion. Reaction.
Rule_2 Activation. Inhibition.
Rule_3 Sensing. Following.

⊢ Pattern. Structure. Form.

Two chemicals. One feeds. One kills. Patterns emerge.

A + 2B → 3B (autocatalysis), B → ∅ (decay)

▼ CLICK. DRAG. WATCH. ▼
PARAMS:
dA = 1.00
dB = 0.50
f = 0.055
k = 0.062

One activates. One inhibits. Both diffuse at different speeds.

∂ₜu = Du∇²u + f(u,v), ∂ₜv = Dv∇²v + g(u,v) | Du ≠ Dv

▼ CLICK. DRAG. WATCH. ▼
PARAMS:
Du = 0.16
Dv = 0.08
f = 0.035
k = 0.060

Many agents. No brain. No plan.

S = (Sₗ, Sᶠ, Sᵣ) → θ₊₁ = θ + RA·sgn(argmax S) → deposit δ

▼ CLICK. DRAG. WATCH. ▼
PARAMS:
N = 30,000
SA = 0.25π
SO = 9
D = 25
δ = 0.992

Function from iteration.
Intelligence from process.
No design required.

Emergence = system + rule + time.