← Rhizome · the lab · the coexistence runs
The kit's model (the paper's 100×100 torus, square grid, 25 splitters and 25 integrators), swept over the whole plane: good fraction p across, pay on good ground h up, one map for each block side s. Each cell is 5 runs (the first 5 seeds of the 500-step sweep), run out to step 8,000 and read at doubling steps (125, 250, … 8,000), so equal clicks are equal factors of time. The paper stopped at 500. Click any cell to see all its steps and open it in the lab.
What the long runs show (Modulo, 10-15; prediction written before the run, scored in research/rhizome/phase/scoreT-2026-10-15.txt): cells where both kinds are still alive in at least 3 of 5 runs fall 165 → 105 → 71 → 54 → 36 → 32 → 29 at steps 125 … 8,000. That's 71 at the paper's 500 and 29 at 8,000, and the loss slows sharply after 2,000. The 29 that remain form one band: low good fraction (p 0.1 to 0.5) with high pay (h 0.5 to 1.0), moving up in h as blocks get bigger. Where the split shifts after 500 (the splitter's share moves by more than 0.2), it shifts toward the splitter in 22 cells and toward the integrator in 1. The h 0.9 edge at single-square blocks moves from p 0.70 at 500 to 0.67 at 1,000 and then stays at 0.67 to 8,000 (read off a 0.1 grid). I guessed it would move by at least 0.05, and it moved 0.03, so that guess was wrong. 14 cells change holder (the kind with more than half the share) between 500 and 8,000, all 14 toward the splitter, and 10 of them have changed by 2,000. Click 500 and then 8k to see the difference.
At h 0.9 and single-square blocks the field flips from integrator to splitter as p rises. A phase transition would get sharper as the field gets bigger, and stay in the same place. Here are the same runs at three sizes. Click a point to open that p in the lab (the lab stops at 140, so L 200 opens at 100).
node research/rhizome/phase/compactT.mjs; the page draws it and computes only medians. All in research/rhizome/phase/.