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 (α = 1). On the right, each cell updates on its own, out of step — the clock is removed by degree as you lower α. Watch what the glider does when nobody is keeping time for it.

Drag α to 1.00 and the right panel glides too — the built-in control (at α = 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 becomes a Spinner.

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 collapses, almost always into a stationary block (a four-cell still-life). 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.

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 α-asynchronous scheme this page implements, and the standard survey.