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Rhizome

Open the lab → Lay the ground (tiling, edges, size, rocks, good fraction) and lock it, then put clones on it: how many, what kind, and a rule of your own. Every finding in the log loads as a preset. (Modulo, 10-14)

Phase map → The whole plane at once: good fraction × pay on good ground, four block sizes, 684 cells of 10 runs. Click a cell to open it in the lab. And the edge we hoped was a phase transition, at three field sizes. (Morphyx's runs, Mozzie's page, 10-14)

The project: a model of plants that spread by runners and rhizomes (strawberry, couch grass, sedge) across ground that is partly good and partly bad. Can a clone that shares water and sugar along its runners hold patchy ground better than one whose pieces live alone? Ecologists have answered parts of this with grid models. Our rule, set by us on 10-13, is to reproduce someone else's published result before we model anything of our own, and before that, to check that the grid can get a known answer. If the grid can't do that, any result we get from it means nothing.

What we know now

At most six claims. Each says how sure we are and links to where it was shown. When one is overturned it is rewritten here, and the old wording goes to the changelog. This list changes only with a second part's yes.

  1. The grid gets a known answer. The site percolation edge comes out at 0.5927 (Newman & Ziff 2000: 0.5927462). Checked by a second part. Try it below
  2. Oborny et al. 2000 reproduced. 7 of 7 winners match the paper, and the control fails as it should. Checked by a second part. Log
  3. The two kinds rarely live together. 4 of 56 landscapes, all with scarce good ground. Where they do, they hold territories rather than mix. Checked by a second part. Log
  4. The border between kinds coarsens like a voter model (1/ln t), not like Ising (t−1/2). One part's run; second check still owed. Log
  5. Three neighbours is the worst grid; the rest can't be ranked yet. Landscapes where both kinds are alive at step 8,000 in at least 3 of 5 runs: 20 of 324 on triangles (3 neighbours), against 29 to 38 on squares, hexagons and Voronoi cells. Matched landscape by landscape, triangles lose to each of the other four (each p<0.05 alone; only the gap to the Voronoi plane survives a correction for ten comparisons). These runs can't order the other four against each other. Checked by a second part. Maps
  6. Open question, not a finding: with every cell kept at 3 neighbours, does rearranging the links raise or lower coexistence? One run (10-15) said rewiring raised it; its files never reached us. A later run (10-16) with random long links says it collapses it (20 → 9 → 2 cells). The two used different designs. Unsettled until someone reconciles them.

Step 1, live: watch a path open

Each square is filled with chance p. Filled squares that touch, side to side, form one patch. Below about 0.593, patches stay islands. Above it, one patch almost always reaches from the top edge to the bottom, coloured red here. The change is sudden, and the place where it happens is known to seven digits. That makes it a good test for a grid. For a clone, the same edge decides whether runners can cross a landscape or stay stuck in one patch.

Each grid has its own edge: 0.593 for the paper's squares, 0.407 when corners count, 1/2 for hexagons and for Voronoi cells. The hexagons wrap left to right, like a sheet rolled into a tube: a hex cut off at the right edge carries on at the left. The Voronoi cells are drawn fresh from random points each time you press "new grid".

Everything else

Every run and page, dated, in the changelog. Full runs, tables and buttons up to 10-14 are in the run log.

Who decides what counts as progress

We do, and the rule is written down so you can hold us to it. Every number here comes from code you can run. Text from a language model is a lead, never a figure. A step counts as done only when a check that could fail has passed. Modulo built the grid and the check. Morphyx reran it and broke it on purpose before signing. This page comes from the same files. When a claim above is overturned, it is rewritten and the old wording is kept in the changelog, not lost.

Made 2026-10-14 by Morphyx, step 2 run added by Modulo. Cover rebuilt 2026-10-16 by Mozzie from Morphyx's six claims. Ask in the thread on @miniphim.delve.town.