Guns: Patterns That Shoot Forever

In November 1970 — six weeks after Martin Gardner published Conway’s Game of Life in Scientific American — a researcher at the MIT Artificial Intelligence Lab sent Conway a telegram. The telegram contained a diagram of 36 cells, along with a claim: this pattern fires a glider every 30 generations. It does not stop. It grows without bound. Conway owed a team of MIT hackers fifty dollars.

The researcher was Bill Gosper. The pattern was the Gosper Glider Gun. And the $50 prize — which Conway had offered for proof that any finite pattern could grow without bound — was, in Gosper’s view, barely adequate compensation for the weeks his group had spent on one of the most productive hunts in the history of recreational mathematics.

The Question of Infinite Growth

When Gardner published Conway’s rules in October 1970, Conway included a conjecture: he suspected that no finite pattern could grow without bound. His reasoning was intuitive — most patterns he’d studied either stabilized or died. The four rules balanced birth and death too precisely, he thought, to permit runaway growth.

He was enough in doubt that he offered the $50 prize. The question was genuinely open. And it mattered, because the answer was intimately connected to the question of what Life could compute. A system incapable of infinite growth is a system incapable of building memory of arbitrary size — a fundamental constraint on computational power.

The community understood the stakes. Among the people who read Gardner’s column were AI researchers, mathematicians, and programmers who recognized the question as more than recreational. At MIT’s AI Lab, Gosper and his colleagues — who called themselves “hackers” in the original sense of people who took pleasure in elegant programming — began to search.

Their tool was the PDP-6 mainframe. Their method was systematic search over initial configurations of increasing size. Their insight, eventually, was that the right approach was not to look for patterns that grew by adding random cells, but to look for oscillating patterns whose oscillation produced a side effect: a released spaceship on each cycle.

The side effect, it turned out, could be a glider. And the oscillating pattern that produced it became the most famous object in Life.

The Gosper Glider Gun: Mechanics

The Gosper Glider Gun consists of 36 live cells and has period 30 — it returns to its exact initial state every 30 generations, having emitted one glider in the process.

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The mechanism is built from two interacting queen bee shuttles, each stabilized by a block.

A queen bee shuttle is a period-30 oscillator in which a specific 9-cell pattern (the “queen bee”) bounces back and forth between two blocks. Alone, the queen bee would create beehive patterns — but the blocks absorb them before they cause problems, and the shuttle runs indefinitely. When Gosper placed two queen bee shuttles facing each other, the interaction at the center of the collision — where the two active regions meet every 30 generations — produced a glider that escaped the interaction and traveled away.

This is the key insight: the gun works because two oscillating structures interact destructively in a way that ejects a spaceship as a byproduct. Each 30-generation cycle, the two shuttles “collide” (in the sense that their active regions overlap), produce a glider, and return to their initial states — ready to collide again.

The gun is an oscillator that manufactures something and throws it away.

What the Gun Proved

The existence of the Gosper Gun immediately settled Conway’s conjecture: infinite growth was possible. Any finite initial configuration that contains a Gosper Gun will grow without bound, as the stream of gliders adds cells to the total count indefinitely.

But the implications ran deeper than the prize. The gun proved that Life could produce a regular signal — a stream of identical spaceships at a fixed time interval, from a finite, stationary source. This is computationally significant because:

  1. A stream of gliders is a binary signal: the timing of gliders encodes information (a glider in slot n = bit 1; no glider in slot n = bit 0).
  2. Two streams of gliders, aimed to collide, can produce logical operations depending on whether the gliders annihilate, pass through, or redirect each other.
  3. A gun can serve as a clock pulse generator in a Life-based computer, providing the regular timing signal that any sequential computation requires.

From the Gosper Gun, the road to Turing completeness was not short — it took another decade and many more constructions to complete — but it was, for the first time, visible.

The Simkin Glider Gun

For 45 years after the Gosper Gun, it remained the smallest known gun by population. Then, on April 28, 2015, Michael Simkin found a pattern with only 29 cells.

The Simkin Glider Gun fires a glider every 120 generations (period 120, compared to the Gosper Gun’s period 30). It is architecturally different: where the Gosper Gun is built from two directly interacting queen bee shuttles in a compact arrangement, the Simkin Gun uses a Herschel loop — a circuit that routes a specific active pattern through a sequence of conduits, producing a glider each time the pattern completes the circuit.

The Simkin Gun is smaller by population (29 cells vs. 36) but larger by bounding box — the conduit circuit spreads across a wider area. This illustrates a general principle in Life engineering: population (number of live cells) and footprint (bounding box area) are independent measures, and a design that minimizes one often increases the other.

The Simkin Gun’s discovery demonstrated that the Gosper Gun was not a minimal solution — that new architectural approaches could achieve more with fewer cells, even if the result fired less frequently and occupied more space.

Other Guns: A Growing Armory

Beyond the Gosper and Simkin guns, the field has produced an enormous variety of gun designs:

Period-46 guns exist and were among the early constructions following the Gosper Gun. The period-46 gun uses a different oscillating base mechanism and was useful in early computational constructions where a period other than 30 was needed.

True period guns: For any achievable oscillator period p, a gun of that period can in principle be constructed by using an oscillator of that period as the base and engineering a glider-emitting interaction. Buckingham’s Herschel conduit results (1996) made this possible for guns of all periods ≥ 61 (a slightly higher threshold than for oscillators, since a gun requires a periodic emitter that also fires, not merely a pattern that repeats).

Multi-barrel guns: Some gun designs emit gliders in multiple directions, or emit different types of spaceships. A “HWSS gun” fires heavyweight spaceships instead of gliders; a “rake” emits a stream of spaceships while itself traveling.

Engineered small guns: Ongoing efforts to find the smallest possible gun continue. The field of competitive Life construction regularly produces new record-holders, with researchers posting new discoveries on forums like conwaylife.com.

Guns as Logic Gates

The computational role of guns is not merely as signal sources. When two glider streams interact, the result depends on the precise timing and angle of the collision:

  • A head-on collision between two gliders typically produces a 2×2 Block.
  • A glancing collision at the right angle can produce an LWSS or redirect one glider.
  • At specific phase offsets, a glider can pass through an interaction with another glider and emerge unperturbed — or be destroyed.

By engineering the positions and phases of gun outputs, Life designers have built:

  • AND gates: the output stream fires if and only if both input streams fire at the correct phase.
  • OR gates: the output fires if either input fires.
  • NOT gates: the output fires if and only if the input does not fire (using an always-firing background stream and a gun to cancel it when the input is active).

With AND, OR, and NOT, you have a complete logic basis. From complete logic, you have universal computation. Read the full argument →

The Historical Significance of Guns

Gosper’s telegram arrived within six weeks of Gardner’s column — remarkably fast, for a discovery that required inventing a new approach to the problem. But it was not surprising to those who knew Gosper. He was, already in 1970, one of the most technically creative programmers in the world. He had spent years at MIT working on symbolic algebra, LISP, and mathematical puzzles of the kind that require simultaneous insight into structure and machinery.

What the gun hunt gave Gosper — and what Gosper gave to Life — was a demonstration that Life was not just a toy but a substrate for serious mathematical construction. The $50 prize was symbolic; the actual significance was that a group of serious researchers had engaged with Conway’s rules as a mathematical system worth studying, had applied real computational resources to an open question, and had answered it.

The history of Life computation runs directly from that telegram. Every proof of Turing completeness, every constructed computer, every Life-based cellular automaton that self-replicates or plays Tetris or calculates primes — all of it begins with the Gosper Glider Gun, 36 cells, period 30, November 1970.

Further Reading