The Substrate, Running
The same pattern, the same rule, one keeps its clock, one loses it
Both panels below run Conway's Game of Life on the same lattice, seeded with the same glider, the small five-cell pattern that is the field's emblem of "emergent," self-propelled order. The only difference is time. On the left, every cell updates in lockstep on a single global clock (u = 1). On the right, each cell updates on its own, out of step, the clock is removed by degree as you lower u. Watch what the glider does when nobody is keeping time for it.
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. These two panels expose no basin of their own. In the left panel every cell updates together (u = 1), and the glider travels forever with its population fixed at five. That is persistence, and nothing here pushes the glider and watches it come back. The right panel removes the clock: move the Right panel u slider below 1 and the glider comes apart, ending as a still pattern or as an empty grid. Where a broken glider ends is a destination. Nothing here pushes that end state to see whether it returns, and the Block shows why that matters: a block pushed off its square does not come back.
Article IV of the Laboratory's Constitution requires every runnable panel to expose a basin, a perturbation and a recover-or-rupture readout. A panel that cannot expose a basin is a reading page, and it must say so. These panels have the perturbation (the u slider) and a readout (the status line above the right panel) and no basin to expose, so under Article IV this is a reading page. A structure that survives without the clock, and comes back when pushed, would be the first basin here.
Synchronous, u = 1
Asynchronous
Drag u to 1.00 and the right panel glides too, the built-in control (at u = 1 the async rule is exactly synchronous). Lower it, and the glider comes apart. When the slider is moved all the way to the left, the glider settles into a still five-cell pattern.
What you are seeing
The left glider travels forever: it is a genuine spaceship of the synchronous rule, and it wraps around the toroidal lattice indefinitely, population fixed at five. The right glider, once the clock is even partly removed, cannot hold itself together, the pattern needs all five cells to update together, and when they don't, it comes apart. From the panel's starting state it most often dies out entirely, at the default setting included, and at some settings it settles into a stationary block (the author believes this may be a standing wave). Over many different starting states, a block forms about half the time. It stops being a glider. This is the well-known Game-of-Life result (Blok & Bergersen; Fatès): the glider's motion was partly the clock's doing, not its own.
That is the entire reason this series was rebuilt on an asynchronous substrate. If the emblem of emergent order is partly a clock artifact, then any structure that "self-organizes" on a globally clocked lattice is under suspicion, it may just be wearing the clock, the way this glider was.
But removing the clock is not a neutral filter, and this very demo shows why. Look at how the glider tends to die: it settles into a block, a stable still-life. Asynchrony destroys some synchronous artifacts (the glider's motion) and, in the same breath, stabilizes others (the block is a fixed point the clock would never have let settle, a documented effect in its own right). So "survives without the clock" is not a proxy for "holds itself together": the block survives, and it pays nothing to do so, it is the dead equilibrium. The real question is not whether a structure persists once the clock is gone, but who is paying to keep it going. That is a measurement, not a demo, and earning it is exactly the burden of the next experiment.
This page proves the substrate, not a theory result. It shows that the engine's clock is real and load-bearing (the control: at u = 1 it exactly reproduces synchronous update; lower u and the dynamics genuinely change). It does not yet show anything about RAPT's self-produced-vs-supplied verdict, that needs a fresh instrumented ecosystem swept across u (the next experiment, gated on the local-tik work). Claiming a self-organization result from a glider demo would be exactly the false confirmation this zone exists to prevent. This is the ground; the experiment is built on it next.
An established result, not a finding
The sync→async collapse shown here is one of the most thoroughly settled methodological cautions in Artificial Life, that synchronous updating can manufacture "emergent" order asynchronous updating dissolves. This page reproduces it as motivation; it claims no part of it. The lineage, and the two-sidedness noted above:
- Ingerson & Buvel (1984), Structure in asynchronous cellular automata, Physica D 10. doi:10.1016/0167-2789(84)90249-5, update order is not neutral.
- Huberman & Glance (1993), Evolutionary games and computer simulations, PNAS 90. doi:10.1073/pnas.90.16.7716, the canonical "the pattern was a synchrony artifact" result.
- Bersini & Detours (1994), Asynchrony induces stability in cellular automata based models, Artificial Life IV (MIT Press), the other half: asynchrony stabilizes as well as destroys.
- Blok & Bergersen (1999), Synchronous versus asynchronous updating in the "Game of Life", Phys. Rev. E 59. doi:10.1103/PhysRevE.59.3876, the specific result these two panels show.
- Fatès (2014), A guided tour of asynchronous cellular automata, J. Cellular Automata 9; arXiv:1406.0792, the asynchronous scheme this page implements (each cell updates with a fixed probability per step), and the standard survey.
Duncan(√2). The left is double-buffered synchronous update; the right updates each cell with probability u per step from the pre-step grid, so u = 1 is synchronous exactly. The reference engine (deterministic, seeded, with a continuous-time Poisson core) is validated in the project's build folder; this page is a faithful in-browser port of it. Downstream/experimental; nothing here touches the framework's canon.