replicators

one agent, dropped in an empty space. every tick, every living agent has a chance to spawn a copy of itself nearby. every copy does the same thing. that's the whole rule — more of this type of thing, which themselves create more — and it's enough to produce a real exponential curve, right up until the space runs out and the curve bends over. RSI in a box roughly 900 pixels wide.

population 1 · gen 0
population 1 / generation 0 ticks elapsed 0 peak growth rate 0/tick growing

still growing — every agent on screen is trying to make one more.