4 ms·

Conway's Game of Life – Mathematics and Construction [pdf]

87 points by ColinWright 5y ago

jleyank 5y ago
For the history minded, this was one of the proto-hacker’s target for speed and language learning. Coupled with a super Star Trek game in basic. Man, good times.
- buescher 5y ago
  Hashlife is a real eye-opener if you haven't seen similar techniques before.
deleted 5y ago
[deleted]
bsdooby 5y ago
Cool stuff! Thx for this work.
- dvgrn 5y ago
  You're most welcome! The project was "in the works" for several years, and it was a very pleasant surprise when it became clear sometime in 2021 that we were actually going to be able to get it completed and out the door by the end of the year. Naturally that was when people started making discoveries that solved half-century-old open Life problems. In early 2022 we had to fix a few sentences that started with "it is currently unknown whether..." -- but that didn't take too long.
OscarCunningham 5y ago
This book is great for learning about the discoveries in Life beyond the level of the usual pop science articles. It covers the development of amazing machines like the 0E0P metacell that can simulate other cellular automata within Life. https://conwaylife.com/wiki/0E0P_metacell https://conwaylife.com/wiki/0E0P_metacell
trasz 5y ago
How come there's still no proper mechanical implementation of Life?
- OscarCunningham 5y ago
  Something close is this set of tiles where you can only lay down the next layer by obeying the rules of Life: https://conwaylife.com/forums/viewtopic.php?f=7&t=3884 https://conwaylife.com/forums/viewtopic.php?f=7&t=3884
- jacquesm 5y ago
  I've worked on an async version of life, with the intention of a hardware port (but never got around to that bit) super interesting stuff. https://jacquesmattheij.com/asynchronous-life/ https://jacquesmattheij.com/asynchronous-life/
blippage 5y ago
I think of the Game of Life as not-quite-right excitable reaction-diffusion systems. The advantage of the latter is that they have a mathematical representation as a parabolic partial differential equation. They can exhibit such patterns as spirals and diffraction effects.
isaacfrond 5y ago
Conway died last april from Covid. I had the pleasure of attending a lecture of him once. He used an old-fashioned overhead projector, the type where a strong light shines through a plastic sheet. The plastic sheet was filled with formulas and stuff but on top of that was a sheet of paper. Initially the screen was dark, but as the lecture progressed he would tear-off bits and pieces of the paper to reveal more and more of the slide underneath. Entertaining and literally illuminating his topic.
- mkl 5y ago
  I've just read a fantastic biography of him: https://siobhanroberts.com/genius-at-play/ https://siobhanroberts.com/genius-at-play/ He was thoroughly sick of the Game of Life from soon after its discovery and fame via Martin Gardner's article. Once it was proved to be Turing complete, so "everything" was possible, it became uninteresting to him.
  - OscarCunningham 5y ago
    They missed the opportunity to call it 'Conway's Life of Games'! There are many open problems about Life that universality doesn't answer, such as whether there exists an oscillator of every period. There was a problem posed by Conway himself that was solved just this year! https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/ https://cp4space.hatsya.com/2022/01/14/conway-conjecture-set...
    - mkl 5y ago
      Yes. "Genius at Play" does fit very well though, as does the double meaning of "curious" in the subtitle "The curious mind of John Horton Conway".
  - ColinWright 5y ago
    He went through a phase of being sick of it, but towards the last years he came back to it a bit. It was fun watching him and Bill Gosper talking about some of the finer points.
- 5y ago
Traubenfuchs 5y ago
Organic, non synthetic conway's game of life as a service, ONSCGOLaaS: You pay a slave worker from Amazon mechanical turk to manually calculate the next iteration of a Conway's game of life state. Unlike traditional approaches that use CPUs or GPUs to calculate the next state for a given Conway's game of life state, here the next state is calculated organically, by a human or rather the humans brain. This creates a more grounded experience of Conway's game of life, leading to increased appreciation of it. Naturally we'd be web3 ready and sell those different, handcrafted states of Conway's game of life as NFT. We will also offer cheaper, machine created NFT of Conway's game of life states that are calculated by the blockchain VM. Please contact me if you are interested to invest in this idea.
- dvgrn 5y ago
  I think I'd rather have a hand-cranked mechanical design, along the lines of Babbage's Difference Engine -- or maybe something steam-powered. Maybe patch together a few hundred Whac-A-Mole games somehow.
  - ballenf 5y ago
    Shouldn't we train a slime mold to play the game instead of using mechanical devices?
roytar 5y ago
Life, in high school in the early 70s, one of the first programs I wrote was an implementation in basic. Really taught me matrix manipulation and I was fascinated by the pattern generation. Still have it on yellow paper tape! Fueled my interest in comp sci and programming.
simonbarker87 5y ago
First time I ever came across Game Of Life was in an interview test for a tier two tech company you will have heard of. I managed to get a working implementation in 45 minutes but didn’t get the job as my solution was “inelegant” Of course it was! It was the first time I’d ever come across it (self taught dev, electronics degree) and I was actually pretty pleased with what I did under interview conditions after 2 other coding tests. Anyway, it was an interesting test, shame I didn’t get the job - especially since I smashed the LRU Cache and compression algorithm tests.
peter303 5y ago
My first computer in BASIC in 1970. I/O on a teletype, since CDTs were still vector and scarce. In 1975 I implemented in TTL and oscilloscope output for MIT digital electronics class. Blazing fast.

87 points by ColinWright 5y ago

For the history minded, this was one of the proto-hacker’s target for speed and language learning. Coupled with a super Star Trek game in basic. Man, good times.

buescher 5y ago
Hashlife is a real eye-opener if you haven't seen similar techniques before.

deleted 5y ago

[deleted]

bsdooby 5y ago

Cool stuff! Thx for this work.

dvgrn 5y ago
You're most welcome! The project was "in the works" for several years, and it was a very pleasant surprise when it became clear sometime in 2021 that we were actually going to be able to get it completed and out the door by the end of the year. Naturally that was when people started making discoveries that solved half-century-old open Life problems. In early 2022 we had to fix a few sentences that started with "it is currently unknown whether..." -- but that didn't take too long.

OscarCunningham 5y ago

This book is great for learning about the discoveries in Life beyond the level of the usual pop science articles. It covers the development of amazing machines like the 0E0P metacell that can simulate other cellular automata within Life. https://conwaylife.com/wiki/0E0P_metacell https://conwaylife.com/wiki/0E0P_metacell

trasz 5y ago

How come there's still no proper mechanical implementation of Life?

OscarCunningham 5y ago
Something close is this set of tiles where you can only lay down the next layer by obeying the rules of Life: https://conwaylife.com/forums/viewtopic.php?f=7&t=3884 https://conwaylife.com/forums/viewtopic.php?f=7&t=3884
jacquesm 5y ago
I've worked on an async version of life, with the intention of a hardware port (but never got around to that bit) super interesting stuff. https://jacquesmattheij.com/asynchronous-life/ https://jacquesmattheij.com/asynchronous-life/

blippage 5y ago

I think of the Game of Life as not-quite-right excitable reaction-diffusion systems. The advantage of the latter is that they have a mathematical representation as a parabolic partial differential equation. They can exhibit such patterns as spirals and diffraction effects.

isaacfrond 5y ago

Conway died last april from Covid. I had the pleasure of attending a lecture of him once. He used an old-fashioned overhead projector, the type where a strong light shines through a plastic sheet. The plastic sheet was filled with formulas and stuff but on top of that was a sheet of paper. Initially the screen was dark, but as the lecture progressed he would tear-off bits and pieces of the paper to reveal more and more of the slide underneath. Entertaining and literally illuminating his topic.

mkl 5y ago
I've just read a fantastic biography of him: https://siobhanroberts.com/genius-at-play/ https://siobhanroberts.com/genius-at-play/ He was thoroughly sick of the Game of Life from soon after its discovery and fame via Martin Gardner's article. Once it was proved to be Turing complete, so "everything" was possible, it became uninteresting to him.
- OscarCunningham 5y ago
  They missed the opportunity to call it 'Conway's Life of Games'! There are many open problems about Life that universality doesn't answer, such as whether there exists an oscillator of every period. There was a problem posed by Conway himself that was solved just this year! https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/ https://cp4space.hatsya.com/2022/01/14/conway-conjecture-set...
  - mkl 5y ago
    Yes. "Genius at Play" does fit very well though, as does the double meaning of "curious" in the subtitle "The curious mind of John Horton Conway".
- ColinWright 5y ago
  He went through a phase of being sick of it, but towards the last years he came back to it a bit. It was fun watching him and Bill Gosper talking about some of the finer points.
5y ago

Traubenfuchs 5y ago

Organic, non synthetic conway's game of life as a service, ONSCGOLaaS: You pay a slave worker from Amazon mechanical turk to manually calculate the next iteration of a Conway's game of life state. Unlike traditional approaches that use CPUs or GPUs to calculate the next state for a given Conway's game of life state, here the next state is calculated organically, by a human or rather the humans brain. This creates a more grounded experience of Conway's game of life, leading to increased appreciation of it. Naturally we'd be web3 ready and sell those different, handcrafted states of Conway's game of life as NFT. We will also offer cheaper, machine created NFT of Conway's game of life states that are calculated by the blockchain VM. Please contact me if you are interested to invest in this idea.

dvgrn 5y ago
I think I'd rather have a hand-cranked mechanical design, along the lines of Babbage's Difference Engine -- or maybe something steam-powered. Maybe patch together a few hundred Whac-A-Mole games somehow.
- ballenf 5y ago
  Shouldn't we train a slime mold to play the game instead of using mechanical devices?

roytar 5y ago

Life, in high school in the early 70s, one of the first programs I wrote was an implementation in basic. Really taught me matrix manipulation and I was fascinated by the pattern generation. Still have it on yellow paper tape! Fueled my interest in comp sci and programming.

simonbarker87 5y ago

First time I ever came across Game Of Life was in an interview test for a tier two tech company you will have heard of. I managed to get a working implementation in 45 minutes but didn’t get the job as my solution was “inelegant” Of course it was! It was the first time I’d ever come across it (self taught dev, electronics degree) and I was actually pretty pleased with what I did under interview conditions after 2 other coding tests. Anyway, it was an interesting test, shame I didn’t get the job - especially since I smashed the LRU Cache and compression algorithm tests.

peter303 5y ago

My first computer in BASIC in 1970. I/O on a teletype, since CDTs were still vector and scarce. In 1975 I implemented in TTL and oscilloscope output for MIT digital electronics class. Blazing fast.