The Bestiary: A Field Guide to Life’s Creatures

When Conway published his rules in 1970, he had no taxonomy. He had a grid, some cells, and a set of four rules — and he had the experience, watching pattern after pattern evolve on a Go board at Cambridge, that something interesting was happening. The creatures came first. The names came later.

The names, when they arrived, borrowed from biology, astronomy, theology, and myth. The study of Life’s patterns acquired the vocabulary of naturalists: still lifes for the inert, oscillators for the rhythmic, spaceships for the mobile. Later came guns (patterns that shoot), methuselahs (patterns that age slowly), and gardens of eden (patterns that cannot have ancestors). This is the language of a bestiary — and the bestiary of Conway’s Game of Life is now, after fifty years of exploration, one of the strangest and richest catalogs in mathematics.

Why Classification Matters

Before you can ask deep questions about a system, you need to know what it contains. The first decade of Life research was, in large part, a cataloging exercise. Conway and his colleagues at Cambridge — Richard Guy, Michael Patterson, and others — spent long evenings tracing the fates of small initial configurations by hand, on graph paper and Go boards, noting what appeared. They were not doing theory; they were doing natural history.

This wasn’t naive. Classification in Life serves the same function it serves in biology: it imposes structure on a space too large to survey directly, enabling hypotheses about why different kinds of things exist and what relationships hold between them. The question “are there oscillators of every possible period?” is only meaningful if you have the concept of an oscillator. The question “can every finite configuration arise as the successor of some other configuration?” is only meaningful if you can imagine patterns that have no predecessor.

The taxonomy didn’t just name things. It created the conceptual vocabulary for the questions that followed.

And the questions that followed were extraordinary. Life turned out to be Turing complete — a universal computer hiding inside four rules. The path to that proof runs directly through the bestiary: you need gliders (spaceships) to carry signals, guns to generate signals on demand, eaters (a variety of still life) to absorb them, and oscillators to time everything. Without the creatures, there is no computer.

The Zoo

Still Lifes: What Survives Forever

The simplest patterns in Life are the ones that do nothing. A still life is a configuration in which every live cell has exactly two or three live neighbors (so it survives), and every dead cell adjacent to the pattern has either too few or too many live neighbors to be born. Both conditions must hold simultaneously, throughout the entire pattern, every generation. It is a global equilibrium achieved through purely local constraints.

The minimum still life is four cells: the Block, a 2×2 square. The next simplest are all six-cell configurations — the Beehive, the Loaf, the Boat, and the Tub. After six cells, the count grows rapidly: 4 distinct still lifes at 7 cells, 9 at 8 cells, 10 at 9 cells, 25 at 10 cells, and over a billion at 24 cells. The enumeration has been completed computationally through 34 cells.

Still lifes are the final state of almost everything. Any finite configuration that doesn’t grow without bound will eventually settle into a mixture of still lifes, oscillators, and departing gliders. The Block is so ubiquitous in this “ash” that it appears roughly once per 473 cells in any large random soup — billions of Blocks form and dissolve and re-form in every large simulation.

But still lifes are not merely debris. They are also the building blocks of every larger construction in Life. The two blocks that stabilize the Gosper Glider Gun are still lifes acting as structural anchors. The “eater” patterns that absorb unwanted gliders in computational circuits are still lifes with a specific geometric property. Understanding still life equilibria is understanding the basic physics of the Life universe.

Read the full still lifes guide →

Oscillators: The Living Heartbeats

An oscillator is a pattern that returns to its exact initial state after a fixed number of generations, called its period, and then repeats forever. It is the simplest form of non-trivial dynamics: not static, not traveling, just cycling.

The Blinker — three cells in a line — is the most common oscillator, discovered by Conway himself in 1969. It flips between horizontal and vertical every generation: period 2. The Toad and Beacon are also period 2. The Pulsar, found by Conway in early 1970, is the most spectacular small oscillator: 48 cells, four-fold symmetry, period 3. The Pentadecathlon — 10 cells in a line that explodes and contracts over 15 generations — is the most elegant known example of a high-period oscillator arising from a trivial starting configuration.

For decades, the question of whether oscillators of every possible period exist drove the field. Some periods were easy — period 2 and period 3 emerge naturally from random soups. Others were maddeningly elusive. In 1996, David Buckingham demonstrated that Herschel conduits could generate oscillators of every period ≥ 58, and in 2013, Mike Playle’s discovery of the “Snark” reflector pushed the threshold down to period ≥ 43. The last gaps — periods 19 and 41 — fell in the summer of 2023 to a team including Nico Brown, Maia Karpovich, and four others. Their paper, posted on arXiv in December 2023, proved that Conway’s Game of Life is omniperiodic: oscillators of every positive integer period exist.

Period 19 and period 41 were found last not because they are especially high, but because they are oddly placed in the landscape of Life’s mechanics — far enough from easily constructible building blocks that no known technique reached them. Their discovery required genuinely new catalysts and, in the case of period 41, the novel idea of using gliders themselves as components of an oscillator.

Read the full oscillators guide →

Spaceships: Patterns That Travel

A spaceship is a pattern that translates across the grid — it returns to its original shape after a fixed period, but shifted in position. No individual cell moves; cells die and are born in the right places to make the pattern appear to travel.

The Glider, five cells, period 4, was discovered by Richard Guy in 1969 or early 1970 while corresponding with Conway about the new rules. It travels diagonally at the maximum possible diagonal speed, c/4. It is the most important pattern in the entire Game of Life — not because of what it is, but because of what it does. A stream of gliders carries a binary signal. Two streams of gliders, precisely aimed, can implement AND, OR, and NOT operations. From that, everything computational follows.

The orthogonal spaceships — LWSS (9 cells), MWSS (11 cells), HWSS (13 cells) — travel at c/2, the maximum possible orthogonal speed, discovered early and now canonical components of any larger construction. Beyond these, an enormous variety of spaceships at various speeds has been found by computer search, including the extraordinary “Caterpillar” (2004, by Jason Summers and others) which travels at the unusual speed of 17c/45.

Speed limits in Life are real and derive from the causal structure of the rules: no influence can propagate faster than one cell per generation. This makes Life a cellular automaton with a genuine “speed of light,” and studying which spaceship speeds are achievable has been an ongoing research program.

Read the full spaceships guide →

Guns: Infinite Production

A gun is a stationary or oscillating pattern that periodically emits spaceships. Guns grow without bound — the spaceships accumulate forever, each one a new addition to the total live-cell count. They are, in the vocabulary of the field, the first examples of unbounded growth.

When Conway published the Game of Life in October 1970, he didn’t know whether unbounded growth was possible. He suspected it might not be, and he offered a $50 prize for proof either way. The prize was claimed in November 1970 by Bill Gosper’s group at the MIT AI Lab.

Gosper’s Glider Gun — 36 cells, period 30 — is the most famous pattern in Life after the Glider itself. It consists of two queen bee shuttles bouncing against each other, stabilized by two blocks. Each collision cycle, lasting 30 generations, produces a glider that escapes the interaction and travels away. The gun runs forever. Its existence proved that finite patterns could produce infinitely many cells, demolishing Conway’s guess and opening a new era in the theory.

For 45 years, the Gosper Gun remained the smallest known gun by population. In 2015, Michael Simkin discovered the Simkin Glider Gun — only 29 live cells, though spread across a larger bounding box, firing period-120. The two guns represent different engineering philosophies: the Gosper Gun is compact and tightly coupled; the Simkin Gun is sparse and architecturally elegant.

Guns are the clocks and sources of Life’s computational machinery. Without a gun to generate a regular stream of gliders, you cannot build a computer. The Gosper Gun is not just a curiosity — it is the foundation of every proof that Life is Turing complete.

Read the full guns guide →

Methuselahs: Long Lives from Simple Starts

A methuselah is a small pattern — typically fewer than 15 cells — that takes a disproportionately large number of generations to stabilize. The name comes from the biblical patriarch who lived 969 years; in Life, a methuselah is a pattern whose lifespan far outlasts its apparent simplicity.

The prototype is the R-pentomino: five cells, arranged in a shape Conway noticed early in his experiments at Cambridge. Five cells is almost the minimum for interesting dynamics — but the R-pentomino doesn’t resolve in a few dozen generations. It churns for 1,103 generations before stabilizing into a configuration of 116 live cells, including six gliders that escape to infinity. When Conway and his colleagues first studied it in 1970, they needed a computer to track it to completion.

Acorn, a seven-cell pattern found by Charles Corderman, runs for 5,206 generations and stabilizes into 633 cells — Corderman’s term for the final configuration was “oak.” The Diehard takes 130 generations and then disappears entirely, leaving not a single live cell. The Rabbits pattern, nine cells, discovered by Andrew Trevorrow in 1986, runs for 17,331 generations.

Beyond these classics, the search for long-lived methuselahs has reached extreme territory. In a 20×20 bounding box, patterns have been found that stabilize after over 126 million generations. These are no longer methuselahs in the original spirit — they are engineered long-livers — but they reveal the extraordinary depth of complexity that Life’s rules can sustain from tiny initial conditions.

The deep insight is that methuselahs are not just curiosities. They are evidence that Life’s rules encode a form of information compression: tiny configurations can store complex futures. The initial entropy of five or seven cells determines the entire subsequent trajectory — 1,103 generations of turbulence, determined completely by the starting arrangement.

Read the full methuselahs guide →

Gardens of Eden: Patterns Without a Past

A Garden of Eden is a valid Life configuration that cannot be the successor of any other configuration. No arrangement of live and dead cells on the infinite grid, evolved forward by one generation, produces a Garden of Eden as output. It exists only as an initial state — it cannot be reached from the history of the universe.

The existence of Gardens of Eden was proved mathematically before anyone knew a specific example. The proof, due to Edward Moore (1962) and completed by John Myhill (1963), works by counting: the number of possible distinct predecessor configurations for an N×N region grows more slowly than the number of possible configurations in that region. For large enough regions, some configurations must be unreachable. The argument does not construct any specific Garden of Eden — it merely guarantees they exist.

The first specific Garden of Eden in Life was identified by Roger Banks and colleagues at MIT in 1971: a pattern fitting in a 9×33 bounding box with 226 live cells. Computer search has progressively reduced the record since then. Achim Flammenkamp found smaller Gardens of Eden in 1991 and 2004. Nicolay Beluchenko found one with 69 cells in an 11×11 box in September 2009. Garden of Eden 6 has 56 cells in a 10×10 box, found in 2011.

Gardens of Eden reveal something fundamental about Life’s relationship to time. Life’s rules are not reversible: applying them forward destroys information. Multiple different configurations can map to the same successor, meaning the map from one generation to the next is not injective. Gardens of Eden are the configurations that nobody maps to — they sit outside the image of the rule-application function. They are evidence that Life has an arrow of time baked into its very structure.

Read the full Garden of Eden guide →

What the Zoo Reveals

The six pattern families are not merely a classification scheme. Together, they describe the full dynamic range of Life — from the inert to the eternal, from the simple to the computationally universal.

What the bestiary reveals, above all, is that emergence in Life is not random. Given the same four rules, the same kinds of things keep appearing. Blocks form constantly, in every soup, in every experiment, on every scale. Gliders emerge everywhere. The Pulsar appears spontaneously from chaotic initial conditions; so does the Pentadecathlon. This is not because anyone designed these patterns into the rules. It is because the four rules, applied locally, have a specific fitness landscape — certain configurations are stable, certain dynamics are self-sustaining, and those configurations and dynamics appear wherever the rules are applied.

This is what complexity theorists mean by attractor: the state space of Life dynamics pulls toward certain structures, and those structures are the creatures in this bestiary.

The deeper implication is philosophical. Conway did not design gliders. He did not design oscillators, or guns, or methuselahs. He designed four rules — and the creatures followed, as inevitably as evolution follows from genetics, competition, and time. The bestiary is a list of things that were, in some sense, already in the rules from the moment they were written, waiting to be found.

The Catalog as Living Research

The enumeration of Life patterns is an ongoing enterprise. The Golly pattern archive contains tens of thousands of named patterns. The Catagolue project, launched by Adam Goucher, has processed over a trillion random soups, cataloging every object that appears — generating statistical tables of which patterns emerge and with what frequency.

In 2023, the proof that Life is omniperiodic closed the last major classification question about oscillators. But the space of possible patterns is infinite, and new records continue to fall: smaller guns, larger methuselahs, tinier Gardens of Eden.

The bestiary is never finished. That’s part of what makes it a bestiary.