Competition
Two producers, one resource. Do they partition the world and coexist, or does one drive the other out entirely?
ADM-A5 §3.6). An authored design claim, not a measurement.
SOV §7.2), what this
panel supplies, not how it scored- out of scope 1 · Recursion lock. There is no self-closing recursive loop here. Two producers compete for empty cells; the dynamic is selection/exclusion under ADM-A5, not a loop that catalyzes its own re-closure.
- exercised 2 · Internal recurcline persistence. The two populations are the basin and the growth sliders are bounded perturbations of it; you can watch the run settle to coexistence or tip to competitive exclusion. Caveat: The update runs synchronously at u=1, so part of the temporal order is supplied by the clock.
- out of scope 3 · Boundary retention. No boundary is modeled. Cell states are producers/empty, not a membrane, and the lattice wraps.
- supplied 4 · Maintenance-bearing continuation. Both producers grow into empty cells at authored rates with no modeled inflow, the shared resource (empty space) is replenished for free by baseline mortality, so nothing pays to persist.
No sovereignty verdict is claimed here or anywhere in this gallery. The Sovereign column is empty, and that emptiness is the honest reading: no panel here has been shown to produce its own order.
The simplest ecological contest: two species, X and Y, both grow into the same resource, the empty space of the lattice, which is finite. Neither eats the other; they simply race for the same ground. When their growth rates are balanced they coexist, partitioning the board into shifting territories. Tip the balance and one species out-races the other into every open cell, competitive exclusion, the classic outcome when two demands press on one shared resource.
On this site a basin is the set of conditions a system comes back from. Push a marble around the inside of a bowl and it rolls back to the bottom; the bowl is its basin, and the rim is its edge, the push beyond which it does not come back. Finding basins, and their edges, is the point of the Laboratory. This contest has two candidate basins, coexistence and exclusion, and the map of territories has none.
| basin | what it returns to | what pushes it | its edge |
|---|---|---|---|
| 1. Coexistence | both X and Y holding ground on the lattice | the growth sliders; Perturb (cull the leader) | growth rates far enough apart that one species out-races the other; no measured setting |
| 2. Exclusion | one species in every open cell, the other at zero | the growth sliders | none seen from inside the run: the lost species stays at zero |
1. Coexistence. When the two growth rates are balanced, X and Y split the board and both persist, which is the status line's default reading, “both persisting, coexistence.” Perturb (cull the leader) knocks back whichever species is ahead; the readout shows whether both species are still holding ground afterwards. The growth sliders change the balance itself. The edge: the slider settings at which coexistence flips to exclusion. Where that flip sits has not been measured. Find it by moving one growth slider away from the other in small steps and watching for one count to reach zero.
2. Exclusion. Tip the balance and the faster species takes every open cell. The slower one goes to zero and stays there: a species with no cells left has nothing to grow from. The edge: none seen from inside the run. Once one species is gone, no slider setting brings it back; only Reset basin does, which is the operator starting the run again.
The territories have no basin. Under coexistence the borders between X and Y keep shifting, and nothing pulls them back to any particular map. What returns is that both species persist.
The two populations are the basin; the growth sliders are bounded perturbations of it. What you can trust is the run's own answer: do both species persist (coexistence), or does one go to zero and stay there (exclusion)?
What you should not read in is a sovereignty verdict, whether either species “pays its own way” is the harder measurement the series keeps gated. This panel shows coexistence-or-exclusion, nothing more.
Two Competitors, One Resource
Duncan(√5), whose anisotropy 𝒜 is shown above (admissible ≤ 0.02).