Self-Replicating Nanorobot Population Control

Replication

Replication rate r 0.35 / s

Carrying capacity K 2500

Resource consumption 1.0×

Kill-Switch (apoptosis)

Kill-switch strength s 0.20 / s

Colony State

Population N

dN/dt

0 / s

Resource: 100%t = 0.0 s

How it works

The colony follows resource-coupled logistic growth with an engineered removal term:

dN/dt = r_eff · N · (1 − N/K) − s · N
r_eff  = r · (R / R0)        (replication slows as resource depletes)
dR/dt  = −c · N              (each nanobot consumes resource per second)

Here N is the live population, K the carrying capacity set by available substrate, r the intrinsic replication rate, R the remaining resource stock (R0 at t = 0), c the per-robot consumption rate, and s the kill-switch removal rate — an engineered apoptosis signal that culls a fixed fraction of the colony per second once activated.

Replication rate r — how fast an individual nanobot can copy itself when resource and room (N ≪ K) both allow it.
Carrying capacity K — the maximum sustainable population for the current substrate; growth flattens as N → K.
Resource consumption — scales c; a hungrier colony depletes R faster, which throttles r_eff and can stall growth even below K.
Kill-switch — the classic proposed safeguard against uncontrolled self-replication ("grey goo"): toggle it on and raise s until dN/dt turns negative and the colony collapses back down.

Integrated with a clamped explicit-Euler step every frame; each visible sphere is one nanobot, instanced and packed into a shell whose radius grows with N^1/3 around the shrinking resource core.

Nanobot (replicating) Nanobot (kill-switch active) Resource core

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