The Modern Pattern Hunt: SAT Solvers, Soup Searches, and the Discoveries They Made Possible

In 1970, Bill Gosper's team found the first glider gun with graph paper, a PDP-6, and weeks of obsessive work. Today, a hobbyist can leave a search program running overnight and wake up to a pattern no human has ever seen. The Game of Life is the same as it always was—the hunt has been utterly transformed.

The past decade has produced a string of landmark discoveries: new spaceship speeds, the first elementary knightship, the reflectors that unlocked omniperiodicity. Behind nearly all of them stand three modern search technologies.

Soup Searching: Discovery by the Trillion

The oldest search strategy is also the most democratic: generate a random field of cells—a "soup"—run it until it stabilizes, and catalog what remains. Most soups settle into the usual ash of blocks, beehives, and blinkers. But once in a very great while, something unprecedented crawls out of the chaos.

The modern incarnation is apgsearch, a distributed search system whose volunteers have collectively censused trillions of soups, with every result aggregated into a public online database called Catagolue. The statistics it produces are a scientific resource in their own right—we now know with extraordinary precision how often nature "invents" a Glider or a Pentadecathlon from random beginnings.

And the rarities keep coming. Soup searches have turned up naturally occurring patterns once thought to be purely artificial—exotic oscillators, rare puffers built on the Switch Engine, and still lifes so improbable they appear once in hundreds of billions of trials. Every soup is a lottery ticket, and the community buys billions per day.

SAT Solvers: Asking Logic Directly

The second revolution came from an unexpected direction: industrial logic solvers. The question "does a spaceship with this speed and this bounding box exist?" can be encoded as a Boolean satisfiability (SAT) problem—millions of clauses relating cell states across a handful of generations. Modern SAT solvers, honed on hardware verification problems, chew through these encodings with astonishing efficiency.

The poster child is Sir Robin. For decades, Life theorists knew that a "knightship"—a spaceship moving two cells over and one cell up, like a chess knight—was possible in principle, but no example was known. In March 2018, Adam P. Goucher, extending a partial result by Tom Rokicki with SAT-based search techniques, completed the first elementary knightship in Life's history. It was a pattern that half a century of human intuition had failed to produce, conjured by translating the question into two million logical clauses.

SAT-driven tools have since become standard equipment, filling in spaceship speeds once thought unreachable. The Copperhead, a compact c/10 spaceship found in 2016 by a forum member running an automated search, and the Loafer, the first c/7 ship, found in 2013, both mark speeds that pure human cleverness never reached in the preceding four decades.

Catalyst Searches: Engineering's Missing Parts

The third technology hunts not for free-standing patterns but for interactions: stable configurations that deflect, transform, or absorb moving objects and then recover. These catalysts are the machine parts of Life engineering.

The greatest triumph of catalyst search remains the Snark, found by Mike Playle in 2013 using his search program Bellman. The Snark reflects a glider by 90 degrees and recovers in just 43 generations—compact, fast, and stable. It became an instant workhorse: adjustable glider loops built from Snarks provide oscillators of almost every large period, and they were essential scaffolding in the march toward the 2023 omniperiodicity proof.

Catalyst searches continue to yield new conduits, reflectors, and "eaters" beyond the classic Eater 1, steadily shrinking the toolkit's components—which in turn shrinks every machine built from them, from glider guns to universal constructors like Gemini's successors.

The Record Books Keep Changing

A snapshot of what modern search has delivered:

• New speeds: c/7 (Loafer), c/10 (Copperhead), and the (2,1)c/6 oblique motion of Sir Robin—the first knightship.
• Omniperiodicity: the final missing oscillator periods, 19 and 41, both fell to targeted searches in 2023, completing a 53-year quest.
• Smaller everything: record-holding syntheses now build most small patterns from a handful of colliding gliders, with costs steadily driven down by automated collision searches.
• Natural rarities: soup censuses keep surfacing "impossible" objects arising spontaneously, blurring the line between engineered and natural patterns.

What Remains Unfound

For all the firepower, Life keeps its secrets. No elementary spaceship is known for most theoretically permitted speeds and directions. Nobody has found a small, fast oblique ship to succeed Sir Robin's ponderous march. The smallest possible Garden of Eden, the cheapest glider synthesis for countless objects, ever-smaller self-replicators—all open.

And that is the enduring lesson of the modern pattern hunt. Each new tool—soup census, SAT solver, catalyst search—was expected to exhaust the interesting questions. Each instead revealed deeper ones. Conway's universe has now absorbed fifty-five years of human and machine ingenuity, and its frontier looks as wide as ever.

The hunt continues. The only thing that changes is the caliber of the telescope.