Learn / Patterns

Pattern encyclopaedia

Every specimen below is a live simulation, not a picture. 34 patterns, each stored in the same RLE format Life software has used since 1980.

Still lifes

Patterns that never change. Every live cell has exactly two or three live neighbours, and every dead cell has anything but three. They are the sediment of Life: run a random soup for a few hundred generations and most of what remains will be blocks, beehives, loaves and boats.

Block

still life

The simplest still life and the most common object in a random soup. Four cells, each with three neighbours - perfectly balanced, going nowhere.

2×2 4 cells

Tub

still life

Four cells around a hole. Add a cell to any corner and you get a boat.

3×3 4 cells

Boat

still life

The smallest still life that is not symmetrical under all four rotations. A boat with one extra cell becomes a long boat; a boat plus a tub becomes a barge.

3×3 5 cells

Barge

still life

Two tubs sharing a diagonal. Barges are members of the same extensible family as boats and ships.

4×4 6 cells

Ship

still life

A diagonal still life. Extendable indefinitely into 'long ships' by inserting more diagonal steps.

3×3 6 cells

Beehive

still life

Six cells in a hexagon. After the block, the second most common thing a random soup settles into.

4×3 6 cells

Loaf

still life

A beehive with a tail. Loaves frequently appear in pairs and fours - a 'bakery' - in the ash left behind by larger reactions.

4×4 7 cells

Eater 1

still life

Also called the fishhook. It swallows an incoming glider and repairs itself in four generations, which makes it the essential building block of Life engineering - every large construction is fenced in by eaters.

4×4 7 cells

Long boat

still life

A boat stretched by one diagonal step. The family continues: very long boat, very very long boat, and so on.

4×4 7 cells

Pond

still life

An eight-cell ring. Ponds often appear as the residue of a collision and sit there forever.

4×4 8 cells

Oscillators

Patterns that return to their starting configuration after a fixed number of generations - the period. A still life is technically an oscillator of period 1. Periods of 2 and 3 are common; long periods are prized, and for decades certain periods were thought impossible until someone finally constructed one.

Blinker

period 2

Three cells flipping between horizontal and vertical. The first oscillator anyone ever sees and still the most common one in random soups.

3×1 3 cells

Toad

period 2

Two offset rows breathing in and out. Period 2, six cells.

4×2 6 cells

Clock

period 2

A four-fold symmetric period 2 oscillator that rotates a quarter turn each generation.

4×4 6 cells

Beacon

period 2

Two blocks touching at a corner. The facing corners wink on and off while the rest stays put.

4×4 8 cells

Pentadecathlon

period 15

Conway found it by running a row of ten cells. Period 15 - unusually long for something so small - and it emits sparks that make it a useful component in larger machines.

10×3 12 cells John Conway, 1970

Octagon 2

period 5

An octagonal ring that pumps in and out on a period of 5.

8×8 16 cells

Figure eight

period 8

Two 3x3 blocks that trade places on a diagonal every four generations.

6×6 18 cells Simon Norton, 1970

Pulsar

period 3

The largest common oscillator: 48 cells with fourfold symmetry, pulsing on a period of 3. Despite its size it turns up naturally in random soups.

13×13 48 cells

Kok's galaxy

period 8

A pinwheel of bars that rotates through a period of 8. Named for Jan Kok, who found it in 1971.

9×9 48 cells Jan Kok, 1971

Spaceships

Oscillators that come back to their original shape displaced by some distance. Speed is measured against c, the theoretical maximum of one cell per generation - a glider travels at c/4 diagonally, the classic spaceships at c/2 orthogonally. Nothing can exceed c, because information cannot propagate faster than one cell per step.

Glider

period 4

Five cells that walk diagonally across the grid, one cell every four generations. Conway's group found it in 1969 and it became the emblem of the whole field - the hacker community adopted it as their symbol in 2003.

3×3 5 cells Richard Guy, 1969

Lightweight spaceship

period 4

The smallest orthogonal spaceship, travelling at half the speed of light. Known as the LWSS.

5×4 9 cells John Conway, 1970

Middleweight spaceship

period 4

One cell wider than the LWSS and just as fast. The MWSS leaves a slightly larger spark, which matters when you are building with them.

6×5 11 cells John Conway, 1970

Heavyweight spaceship

period 4

The largest of the three classic orthogonal ships. Add another segment and it becomes unstable - which is why the family stops here.

7×5 13 cells John Conway, 1970

Copperhead

period 10

A c/10 orthogonal spaceship found in 2016 by a user known only as 'zdr' - proof that after half a century the search space is still giving up surprises.

8×12 28 cells zdr, 2016

Guns

Patterns that return to their original state while emitting spaceships. Because their output is unbounded, guns were the disproof of Conway's conjecture that no pattern could grow forever - and, once you can emit gliders on demand, you can build logic.

Gosper glider gun

period 30

The pattern that won Conway's $50 prize. Bill Gosper's team at MIT found it in November 1970, proving that a Life population can grow without limit - and, by extension, that Life can compute anything a computer can. It fires one glider every 30 generations, forever.

36×9 36 cells Bill Gosper, 1970

Methuselahs

Small patterns that take an extraordinarily long time to settle. The name is the point: a handful of cells that runs for thousands of generations, throwing off gliders and debris, before finally going quiet. They are the clearest demonstration that in Life you cannot predict the outcome without running it.

R-pentomino

methuselah

Five cells that refuse to settle. It runs for 1,103 generations, throws off six gliders, and finishes as 116 cells of debris. Conway's group traced it by hand on a Go board before they had a computer to do it.

3×3 5 cells John Conway, 1969

Thunderbird

methuselah

A simple, symmetric starter that runs for 243 generations.

3×5 6 cells

B-heptomino

methuselah

A seven-cell fragment that appears constantly inside larger reactions. It runs 148 generations and leaves a glider behind - which is why Life engineers treat it as a standard component.

4×3 7 cells

Herschel

methuselah

Named by Conway for its resemblance to a symbol used by William Herschel. Herschel tracks - long chains of still lifes that shuttle a Herschel around a circuit - are the backbone of large-scale Life circuitry.

3×4 7 cells John Conway

Acorn

methuselah

Seven cells that take 5,206 generations to stabilise, ending as 633 cells spread over a huge area. Charles Corderman's classic demonstration that tiny inputs can have enormous consequences.

7×3 7 cells Charles Corderman, 1971

Diehard

methuselah

Seven cells that vanish completely after exactly 130 generations. No pattern of seven or fewer cells is known to last longer before dying out entirely.

8×3 7 cells

Rabbits

methuselah

Nine cells, 17,331 generations. Found by Andrew Trevorrow in 1986 and one of the longest-lived small methuselahs known.

7×3 9 cells Andrew Trevorrow, 1986

Bunnies

methuselah

A nine-cell methuselah that runs for 17,332 generations - one better than Rabbits, which is exactly the sort of margin this hobby is fought over.

8×4 9 cells Robert Wainwright, 1971

Growth and oddities

Everything that does not fit the standard categories - including the smallest known patterns that grow without limit.

Callahan's infinite growth

misc

Ten cells inside a 5x5 box that grow forever - the smallest bounding box known to do so. Paul Callahan found it in 1995 by exhaustive search.

5×5 13 cells Paul Callahan, 1995

Categories you will meet elsewhere

The catalogue above covers what turns up naturally. Life enthusiasts have named a great deal more, and these terms appear constantly in the literature:

Puffer
A spaceship that leaves debris behind it as it travels. The first, the puffer train, was found by Bill Gosper in 1971.
Rake
A puffer whose debris is spaceships. A rake is a gun that moves.
Breeder
A pattern whose population grows quadratically - typically a puffer that leaves guns behind, each of which then emits gliders forever. Gosper found the first in 1971.
Sparker
An oscillator that produces a transient cell or two on its edge each cycle. Sparks do nothing on their own but can perturb a passing object, which makes sparkers essential engineering components.
Eater
A still life that destroys an incoming object and repairs itself. The fishhook eater absorbs a glider in four generations.
Reflector
A construction that changes the direction of a passing glider. Reflectors turn gliders into routable signals - the basis of every large Life circuit.
Wick and agar
Wicks are one-dimensional repeating patterns that burn from one end; agars are two-dimensional periodic backgrounds that fill the plane.
Ash
The stable and oscillating junk left over when a random soup settles. The statistics of ash - which objects appear and how often - are a genuine field of study.
Soup
A random starting configuration. Distributed searches like Catagolue have run trillions of soups looking for objects nobody has seen before, and they are still finding them.

Build your own

Everything here can be pulled into the Lab, edited, and saved back to the gallery under your own account. New oscillators and spaceships are still being discovered by amateurs - the search space is nowhere near exhausted.