For 48 years every elementary spaceship known in Conway's Game of Life moved either orthogonally or diagonally. Oblique ships did exist, but only as vast engineered structures assembled from gliders and circuitry, like the Waterbear, not as compact elementary patterns. Some players who had tried searching doubted an elementary oblique ship existed at all.

Brute force was hopeless, and so was the obvious smarter idea: genetic search. Nearly every random configuration in Life dies out, evolution is extremely sensitive to initial conditions, and the overwhelming majority of the search space has zero fitness, leaving no gradient for a genetic algorithm to climb.

The discoverer instead made it a satisfiability problem. A program called ikpx, part of his MetaSAT project, posed finding an oblique glider as a set of SAT constraints: the Life transition rules, the requirement that the pattern displace two cells horizontally and one vertically every six generations, the proven minimum period for that slope, and the boundary of the search region. Heuristic constraints, such as searching for a long-and-thin ship rather than an arbitrary shape, cut the space down, and ikpx handed the resulting ball of constraints to a modern SAT solver.

The solver returned Sir Robin, catalogued on the Life Wiki as 282P6H2V1: the first elementary oblique glider and the first elementary spaceship with a new slope in 48 years, moving at the maximum speed possible for its slope. The code was published, community members reported an eater and a detector already built, and the discovery drew 733 points and 143 comments on Hacker News.

Don't brute-force or evolve the pattern; encode 'exists a ship with this displacement' as SAT constraints and let a solver search

Encoding 'find a pattern' as satisfiability hands the search to SAT solvers that decades of research have made surprisingly powerful.

Heuristic constraints such as long-and-thin instead of arbitrary shape remove the overwhelming majority of candidate space without excluding the target class.

Targeting a (2,1) displacement with its proven six-generation minimum meant the search aimed at the fastest possible oblique ship, so the first success settled the 48-year question outright.

Brute force and genetic search had no traction because almost every Life pattern dies and tiny changes cascade, while constraint search needs no fitness gradient.

The result was elementary and compact enough to be a useful building block, and the open code and interactive viewers let the community verify and build on it.

When a search space has no gradient and almost no survivors, don't sample it blindly: encode existence as constraints, cut the space with domain heuristics, and let a solver do the exploring

Sir Robin was announced on the Conway's Life forums on 6 March 2018 and posted to Hacker News on 8 March, drawing 733 points and 143 comments; commenters quoted the forum calling it the first elementary spaceship with a new slope in 48 years and noted it came 14 years after the almost-knightship. The Life Wiki catalogued it as 282P6H2V1, community members reported an eater and a detector already built, and a knightship gun or glider synthesis was judged likely to be orders of magnitude harder. The ikpx and MetaSAT code that found the pattern was published on GitLab.

FOLLOW THE EVIDENCE

The sources

  1. Elementary Knightship found in Conway's Game of Life news.ycombinator.com
  2. 282P6H2V1 (Sir Robin) conwaylife.com