A Computer In The Game Of Life

We often hear the term “Turing-complete” without giving much thought as to what the implications might be. Technically Microsoft PowerPoint, Portal 2, and Magic: the Gathering all are Turing-complete, what of it? Yet, each time someone embarks on an incredible quest of perseverance and creates a computer in one of these mediums, we stand back in awe.

[Nicolas Loizeau] is one such individual who has created a computer in Conway’s Game of Life. Unlike electricity, the Game of Life uses gliders as signals. Because two orthogonal gliders can cancel each other out or form a glider eater if they intersect with a good phase shift, the basic logic gates can be formed from these interactions. This means the space between gates is crucial as signals need to be in phase alignment. The basic building blocks are a period-60 gun, a 90-degree glider reflector, a glider duplicator, and a glider eater.

All the Python code that generates these structures is on GitHub as the sheer size of the machine couldn’t possibly be placed by hand. The Python includes scripts to assemble the basic programs as a bank of selectable glider generators. It’s all based on Golly, which is an excellent program for simulating Conway’s Game of Life, among other things. While this isn’t the first computer in the Game of Life as [Paul Rendell] published a design in 2000 and [Adam Goucher] published a Spartan universal computer constructor in 2009, we think this is a particularly beautiful one.

The actual architecture has an 8-bit data bus, a 64-byte memory with two read ports, a ROM with 21 bits per line, and a one-hot encoded ALU supporting 8 different operations. Instructions have a 4-bit opcode which is decoding in a few different instructions. The clock is four loops, formed by the glider reflectors as the glider beams rotate. This gives the computer four stages: execution, writing, increment PC, and write PC to memory.

The Game of Life is an excellent example of Cellular Automaton (CA). There are several other types of CA’s and the history behind them is fascinating. We’ve covered this field before and delved into this beautiful fringe of computer science. Check out the video below to truly get a sense of the scale of the machine that [Nicolas] has devised.

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Watch Conway’s Game Of Life Flutter Across A Flip-Dot Display

Like many of us, [John Whittington] was saddened with the news that John Horton Conway passed away a little earlier this year, and in honor of his work, he added the Game of Life to a flip-dot display that he has been working on. The physicality of an electromechanical display seems particularly fitting for cellular automata.

Like what you see? If you’re curious about what makes it all tick, the display shown is an Alfa-Zeta XY5 28×14 but [John] is currently working on building them into a much larger 256 x 56 display. GitHub hosts the flip-dot simulator and driver software [John] is using, and the Game of Life functions are here.

If you’re new to the Game of Life and are not really sure what you’re looking at, [Elliot Williams] tells you all you need to know in his writeup celebrating its profound impact and lasting legacy. Watch the flip-dot display in action in the video embedded below.

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The Game That Launched 1,000 Hackers

John Conway passed away this week. Even if you don’t know much about mathematics, you will probably know nearly everyone’s favorite cellular automata ruleset: Conway’s “Game of Life”. It’s so much a part of our cultural history, that proto-hacker Eric Scott Raymond suggested using the glider as the hacker emblem.

The idea that a very simple set of rules, applied equally and everywhere, could result in “life” was influential in my growth as a young hacker, and judging from the comments on our article about Conway, I’m not alone. But I won’t lie: I was a kid and thought that it could do much more than make pretty patterns on the screen. I was both right and wrong.

Although amazingly complex machines can be built in Conway’s Life, just check out this video for proof, in the end no grand unifying theory of cellular automata has emerged. As a research topic Conway’s chosen field of mathematics, cellular automata is a backwater. It didn’t really go anywhere. Or did it?

Implementing Conway’s Life in BASIC on a Tandy Color Computer was one of the first things that launched me on my geeky path. It ranks with MENACE: the matchbox-based machine learning algorithm from the 1960’s and an introduction to Markov Chains in the form of a random text generator in my young algorithmic life, all of which I incidentally read about in Martin Gardner’s column in “Scientific American”. Conway’s Life, along with some dumb horse-race game, also taught me about bad random-number generators: the screen would populate the same “randomly” every time on the old CoCo.

So maybe Conway didn’t want to be remembered just for his “Life” because it was a bit of a mathematical dead-end. But in terms of its impact on the world, an entire generation of hackers, and my own personal life, it was able to fill up significantly more than a screen full of pixels. Here’s to Conway, his “Life”, and everyone else who is inspiring the next. You’re not just gliders, you’re glider guns!

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[Game of Life example shown in this article is John Conway’s Game of Life – 1.0 written in Python by Nick Jarvis and Nick Wayne]

John Horton Conway, Creator Of Conway’s Game Of Life, Has Died

Programmers everywhere are familiar with Conway’s Game of Life: whether they’ve written a version themselves or simply seen the mesmerizing action resulting from the cellular automata, it’s a household name in all homes where code is spoken. On Saturday April 11th, 2020 its inventor and namesake, John Horton Conway passed away from COVID-19 at the age of 82.

Born in Liverpool, Conway received his PhD in mathematics in 1964 from Gonville and Caius College, Cambridge. He accepted a position at Sidney Sussex College, Cambridge which he held until joining the faculty of Princeton University in 1987. A brilliant mathematician, he received numerous awards and was well known for his work in combinatorial game theory, group theory, and theoretical physics.

Many readers will be familiar with his Doomsday algorithm which can be used to deduce the day of the week for any given date in your head. But by far the rockstar mathematics moment of developing Conway’s Game of Life in 1970 cements him a perpetual place of legend in computing lore. His original work on the concept used pencil and paper as the computing revolution had yet to make digital resources easily available, even to mathematics researchers like Conway.

The game uses an infinite grid of squares where all of the edges of the grid wrap around. Four simple rules (which can be boiled down to three if you’re clever) determine which cells live and which cells die during each frame of the “game”. The only parameters that are needed are the number and position of living cells at the start of the game, and the delay between each game frame. But the effect of this simplicity is not to be understated. The game can be coded by a novice — and it’s become a common challenge in University course work. Small errors, or intentional tweaks, in the implementation have profound effects on behavior of the game. And the effect on the person programming it for the first time can be long lasting. You could call it a mathematics gateway drug, grabbing the curiosity of the unsuspecting mind and pulling it down the rabbit hole of advanced mathematics discovery.

We’d love to celebrate his life by hearing your own stories of programming the Game of Life in the comments below. If you haven’t yet had the pleasure, now’s a great time to take on the challenge.

[Game of Life example shown in this article is John Conway’s Game of Life – 1.0 written in Python by Nick Jarvis and Nick Wayne]

A Stylish Coffee Table Featuring Conway’s Game Of Life

Coffee tables are a great place to put your hot beverages, but most don’t offer a lot beyond that. For most people this is perfectly acceptable, but hackers often desire a little more. [Andrei Erdei] is one such person, who built Conway’s Game of Life into this handsome piece of furniture.

The build began with an existing coffee table, chosen for its glass top. Unfortunately, the top was painted black on one side, and was completely opaque, negating its use as a diffuser for LEDs. Instead, this was replaced with smoked glass, with frosted window film applied to make the final piece darker. This attention to detail allowed [Andrei] to install the WS2812B LED strips underneath such that they’re invisible when switched off. The LEDs themselves are run by a WEMOS D1 mini, based on the ESP8266. This microcontroller has plenty of grunt, which makes running the LEDs and the Game of Life code a cinch.

If you want to make something attractive and blinky, it’s hard to go wrong with Conway’s Game of Life. You can even use it to make a clock or a synthesizer; or build an entire game of Tetris within it. Video after the break.

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Tiny ThinkPad Plays Tiny Games

[Paul Klinger] can’t seem to get enough of building tiny, amazing gaming rigs, and we love him for that. They combine two of our favorites: miniatures and portable gaming. His newest creation honors the form of the formidable ThinkPad.

Of course it has the red nipple and lid LED—wouldn’t be a ThinkPad without ’em. ThinkTiny’s nipple is a 5-way joystick that plays Snake, Tetris, Lunar Lander, and more on an OLED screen. Like its predecessor the Tiny PC, [Paul] used an ATtiny1614, which (FYI) has a new one-wire UDPI interface. He can easily reprogram it through pogo pin holes built into the case.

There are some nice stylistic details at play here, too. The lid LED is both delivered and diffused by a 2mm grain of fiber-optic cable. And [Paul] printed the cover with a color change to transparent filament to make the Think logo and the charging LEDs shine through. Maneuver your way past the break to see it in action.

If you haven’t leveled up to AVR programming yet, introduce yourself to Arduboy.

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Building A Working Game Of Tetris In Conway’s Game Of Life

If you haven’t been following along with Conway’s Game of Life, it’s come a long way from the mathematical puzzle published in Scientific American in 1970. Over the years, mathematicians have discovered a wide array of constructs that operate within Life’s rules, including many that can be leveraged to perform programming functions — logic gates, latches, multiplexers, and so on. Some of these creations have gotten rather huge and complicated, at least in terms of Life cells. For instance, the OTCA metapixel is comprised of 64,691 cells and has the ability to mimic any cellular automata found in Life.

A group of hackers has used OTCA metapixels to create a Tetris game out of Life elements. The game features all 7 shapes as well as the the movement, rotation, and drops one would expect. You can even preview the next piece. The game is the creation of many people who worked on individual parts of the larger program. They built a RISC computer out of Game of Life elements, as well as am assembler and compiler for it, with the OTCA metapixels doing the heavy lifting. (The image at the top of the post is the program’s data synchronizer.

Check out the project’s source code on GitHub, and use this interpreter. Set the RAM to 3-32 and hit run.

For a couple of other examples of Life creations, check out the Game of Life clock and music synthesized from Life automata we published earlier.