Penrose’s Game of life

Conway’s Life a “no-player, never-ending game.”

How to play #The-Game: Level 1–5

B.M.R. Heijligers
6 min readMar 13, 2021


You can find the instruction manual in the basement…

A model of Reality by Dirk F. Meijer

Level 1

Conway: It’s turtles all the way down!

The game was simple: Place any configuration of cells on a grid, then watch what transpires according to three rules that dictate how the system plays out.

Birth rule: An empty, or “dead,” cell with precisely three “live” neighbors (full cells) becomes live.

Death rule: A live cell with zero or one neighbors dies of isolation; a live cell with four or more neighbors dies of overcrowding.

Survival rule: A live cell with two or three neighbors remains alive.

With each iteration, some cells live, some die and “Life-forms” evolve, one generation to the next.

John Horton Conway, investigating “Life” in 1974. Credit: Kelvin Brodie/The Sun News Syndication

Among the first creatures to emerge was the glider — a five-celled organism that moved across the grid with a diagonal wiggle and proved handy for transmitting information. It was discovered by a member of Dr. Conway’s research team, Richard Guy, in Cambridge, England. The glider gun, producing a steady stream of gliders, was discovered soon after by Bill Gosper, then at the Massachusetts Institute of Technology.

The Martin Gardner Literary Interests/Special Collections, Stanford University Libraries

In 2018, there was a much-celebrated discovery of a special kind of spaceship, the first elementary knightship, named Sir Robin. Made of hundreds of cells, it moves two cells forward and one sideways every six generations. It was discovered by Adam P. Goucher, a British algorithmist, building on an earlier partial find by Tomas Rokicki, a developer of Golly, a program for exploring the distant future of large Life patterns.

And the hunting party continues. In September, Pavel Grankovskiy, of Russia, discovered the Speed Demonoid spaceship. In December, John Winston Garth, of Alabama, discovered the Doo-dah spaceship. Both are contenders for pattern of the year, in what has been a good year for new Life discoveries.

Level 2

Bill Gosper

— Mathematician and programmer, Stanford, Calif.

Life is the world’s most wholesome computer game! True, it used to be dangerously addicting to some of us, but not so much now that nearly all of the theoretically possible gun and oscillator periods have been found. It took 40 years to find the coveted Snark, a stable pattern that reflects gliders 90 degrees.

But there are still open questions: for example, what spaceship vector velocities are possible, or what constructions are possible with glider collisions. A startling recent theorem states that any construction, no matter how large, can be accomplished with a reverse caber-tosser built from a certain fixed number of gliders — that number was 32, but as of September it is now down to 17.

Level 3

Brian Eno

Musician, London

I first encountered Life at the Exploratorium in San Francisco in 1978. I was hooked immediately by the thing that has always hooked me — watching complexity arise out of simplicity.

Life ought to be very predictable and boring; after all, there are just three simple rules that determine the position of some dots on a grid. That really doesn’t sound very interesting until you start tweaking those rules and watching what changes.

Life shows you two things. The first is sensitivity to initial conditions. A tiny change in the rules can produce a huge difference in the output, ranging from complete destruction (no dots) through stasis (a frozen pattern) to patterns that keep changing as they unfold.

The second thing Life shows us is something that Darwin hit upon when he was looking at Life, the organic version. Complexity arises from simplicity! That is such a revelation; we are used to the idea that anything complex must arise out of something more complex. Human brains design airplanes, not the other way around. Life shows us complex virtual “organisms” arising out of the interaction of a few simple rules — so goodbye “Intelligent Design.”

Level 4

Melanie Mitchell

Professor of complexity, Santa Fe Institute

Given that Conway’s proof that the Game of Life can be made to simulate a Universal Computer — that is, it could be “programmed” to carry out any computation that a traditional computer can do — the extremely simple rules can give rise to the most complex and most unpredictable behavior possible. This means that there are certain properties of the Game of Life that can never be predicted, even in principle!

In this moment in time, it’s important to emphasize that inherent unpredictability — so well illustrated in even the simple Game of Life — is a feature of life in the real world as well as in the Game of Life. We have to figure out ways to flourish in spite of the inherent unpredictability and uncertainty we constantly live with. As the mathematician John Allen Paulos so eloquently said, “Uncertainty is the only certainty there is, and knowing how to live with insecurity is the only security.” This is, I think, Life’s most important lesson.

The Martin Gardner Literary Interests/Special Collections, Stanford University Libraries

Level 5

Daniel Dennett

Professor of philosophy, Tufts University

I use the Game of Life to make vivid for my students the ideas of determinism, higher-order patterns and information. One of its great features is that nothing is hidden; there are no black boxes in Life, so you know from the outset that anything that you can get to happen in the Life world is completely unmysterious and explicable in terms of a very large number of simple steps by small items. No psionic fields, no morphic resonances, no élan vital, no dualism. It’s all right there. And the fact that it can still support complex adaptively appropriate structures that do things is also important.

In Thomas Pynchon’s novel “Gravity’s Rainbow,” a character says, “But you had taken on a greater and more harmful illusion. The illusion of control. That A could do B. But that was false. Completely. No one can do. Things only happen.”

This is compelling but wrong, and Life is a great way of showing this.

In Life, we might say, things only happen at the pixel level; nothing controls anything, nothing does anything. But that doesn’t mean that there is no such thing as action, as control; it means that these are higher-level phenomena composed (entirely, with no magic) from things that only happen.

This is where Dennett and I diverge. I believe Conway’s Game of Life shows precisely that the story of a singular cause and effect narrative is false when described from a perspective within the game and in the language of describing “objects” and events.

From the perspective of the “objects” within the game, the existence of the board is not visible.

Hence the phrase “There is no spoon”

It could be that any deeper expression of the structure of reality can only be expressed within the game in a language that is completely relational and procedural.

With as penultimate ironic possibility that both language and physical reality could seen from a unified perspective as Stuart Hameroff is referring to in minute 7:21 of this video.

Stephen Wolframs meta-mathematical model of generalized cellular automata offers a first possible candidate for such a unified perspective.

(198) Computation and the Fundamental Theory of Physics — with Stephen Wolfram — YouTube

(Discrete) Time will tell us.



B.M.R. Heijligers

Cosmologist gone #Rogue. Embodiment coach for the technologically gifted. Voor Nederland: Drs. B. — Sterrenkundige en #WetenschapsFilosoof.