Game of Life: Logic gates

Alex Bellos
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The logic gates NOT, AND and OR in the Game of Life.
The Game of Life is a cellular automaton invented by John Conway in the late 1960s.
I write about it in my book Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life:
The book has the US title The Grapes of Math:



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Comentários 38
Cheeseburger Monkey
Cheeseburger Monkey 23 dias atrás
0:16 you sound awfully familiar...
Entity Valkyrie 2 - Fixing Your Flags version 2
That’s too basic for a Game of Life expert like me. ( I am quite well known in Conway Life community. My user page is just above. I created a period-11040 spider gun on January 2020.
GODZILLA godzilla
GODZILLA godzilla 2 meses atrás
How do you switch signals without manually interfering with the eaters?
Nathan Brader
Nathan Brader 5 meses atrás
3:44 "What to know more?"
Noir GuitarSuperstar
Noir GuitarSuperstar 6 meses atrás
Learn to use a microphone.
Uroš Janković
Uroš Janković 10 meses atrás
Great! Now make a computer that can run Conway's game of life
Franklin Hunt
Franklin Hunt 9 meses atrás
Well, Conway's Game of life has been simulated in Conway's Game of life
Antek Borkowski
Antek Borkowski Anos atrás
It means you can program game of life in Conway's game of life
TavernGaming 8 meses atrás
Its been done
Joe Dempsey, Sr.
Joe Dempsey, Sr. Anos atrás
I find your demonstration to be most unsatisfying. The so-called "output" originates from different sources in many cases and often directed in different directions. To be truly analogous to a logical gate, the inputs should control a single output so that this output could then be routed to another gate.
OskarnikPL Anos atrás
Stop spitting in the microphone!
John Jackson
John Jackson Anos atrás
I was looking for something like this the other day! Thank you!
코딩랩 CodingLab
funny thinking!
Rask R
Rask R Anos atrás
If you have NOT and OR gates you can reacreate every other gate. With all gates you can make basic calculations. With calculator you can make programmable computer. With computer you can code game of life. Return to first sentence.
now we wait for a cpu
ALazySquirrel 2 anos atrás
Isn't the second gate a NOR gate?
WilmoTheBear 2 anos atrás
Only thing i understand about this video is that you need a better microphone.
Redstoneboi 2 anos atrás
you can simulate anything with only NAND or NOR gates. NOT and AND gates can create NOR gates and NAND gates. NOT and OR gates can create NAND gates and NOR gates.
Pierre-Alexandre Ponant
Mind blowing
Sam Cornwell
Sam Cornwell 2 anos atrás
Hey Alex, good video. I don't want to undermine it or anything but you sound just like David Mitchell
Youcef Khalil MOHAREM
Youcef Khalil MOHAREM 2 anos atrás
Astonishing Science!
dustin chiasson
dustin chiasson 2 anos atrás
How about a flip-flop?
Redstoneboi 2 anos atrás
#N Boat-bit #C A reaction that shows how boats (along with a snake or aircraft car #C rier) can be used to represent a 0 or a 1 and glider collisions can #C be used to read and write the bit. #C x = 25, y = 24, rule = 23/3 6bo18b$7bo17b$5b3o17b8$16bo8b$14bobo8b$10b2o3b2o8b$11b2o12b$10bo10bob 2o$21b2obo6$bo23b$b2o22b$obo! open this in golly.
ophello 2 anos atrás
Dude -- get a pop silencer.
heimdall1973 2 anos atrás
To build a computer circuit (or start with a calculator) you also need something that will change the direction of gliders. Also, there is a much smaller NOT gate: if a glider hits the Gosper's glider gun at the right place, it prevents formation of one glider but keeps the gun going.
Redstoneboi 2 anos atrás
inline inverter reaction?
heimdall1973 2 anos atrás
On this "racetrack", look at the two uppermost glider guns. The left one forms a NOT gate similar to the one in this video, but the right one is what I meant: it's supposed to shoot gliders into up-right direction but most of the time it's hit by a glider from bottom left which prevents it from creating a glider. Every now and then there is a gap (because a glider arriving towards the left gun annihilates one of its gliders), which therefore allows glider creation. The video also demonstrates how to change direction (bend wires) for the circuit. On the bottom you can see that the wire can also be horizontal or vertical, not just diagonal.
quintopia 2 anos atrás
Is this the construction for Conway's original proof of universality?
slap_my_hand 3 anos atrás
Someone needs to build a CPU with this. Or at least a glorified calculator.
Aaron Hollander
Aaron Hollander Anos atrás
Ian Golsby ... how far did you get?
Ian Golsby
Ian Golsby 2 anos atrás
I'm about to start making all the logic gates, then probably a 4 Bit add/subtract unit. The main difficulty would probably be syncronizing the times.
KacperParkour 3 anos atrás
AaronThePerson 3 anos atrás
btw what website is this?
Redstoneboi 2 anos atrás
it's a program.
AaronThePerson 3 anos atrás
I like to think of the gliders as little armies.
Redstoneboi 2 anos atrás
see gosper's breeder for an intense army
Guy Eldar
Guy Eldar 3 anos atrás
nice video! I noticed you could also make a 'xor' gate by altering the 'or' gate a bit. just make input A shoot to the left side, and then when both A and B have an input all gliders are canceled. its just more efficient than building 'xor' out of the other gates.
Girl More
Girl More 3 anos atrás
How to split signal and cross wire
Redstoneboi 2 anos atrás
*there are no crossovers, these don't travel on wires. however, if you want signals to cross without interaction, here's an RLE that you can open in Golly:* #C p30 glider crossing demo #C This demonstrates a device which allows 2 p30 data streams to cross #C each other. It uses 3 copies of a remarkably simple p30 signal #C duplicator found by Dieter Leithner. #C #C The crossing works as follows: Let the input signals be A and B, #C with A on the left. Both inputs are copied and inverted; we now #C have -A, -A, -B, -B. The middle signals cross in a vanish reaction #C (and one output is discarded), giving -A, A&-B, -B. The left two #C signals can now cross each other since they're never both 1. Next, #C -A is copied and inverted, giving A&-B, A, A, -B. Another vanish #C reaction gives -A&-B on the right, which can safely cross A, #C yielding A&-B, -A&-B, A. The signal on the left is inverted and #C crosses the middle signal in a vanish reaction, producing #C -(A&-B) & -(-A&-B) = B. #C #C In this demo, the inputs come from a p150 (2-on, 3-off) gun aimed #C southeast p180 (3-on,3-off) gun aimed southwest. #C Dean Hickerson, 9/4/96 x = 188, y = 205 158bo$157bobo$156bo3b2o6b2o$145b2o9bo3bob2o4bobo$31b2o112b2o9bo3bob3o 4b3o$31bo2bo122bobob2o2bo4b3o6b2o$17bobo15bo122bo4b2o4b3o7b2o$15bo3bo 2b3o10bo6b2o124bobo$15bo19bo6b2o124b2o$8b2o4bo4bo7b2o2bo2bo$8b2o5bo7bo bo2bo2b2o122bo$15bo3bo5b3o127bobo8bo$17bobo135b2o7b3o$163bo$163b2o$34b o$22b2o11bo$23bo9b3o112bo$23bobo121bo$24b2o121b3o8b2o$157b2o$31bo127bo $31b2o$30bobo9bo$40bobo$41b2o97bo$140bobo23bo$140b2o23b2o10b2o$165bobo 9b2o$23b2o135b2o12b2o6bo3b2o$24b2o23bo108bo3bo10b3o5bo3bobo$23bo6b2o 18bo101b2o3bo5bo10b2o6b5o$12b2o16bo17b3o82bo18b2o2b2obo3bo13b2o4b3o$ 11bo3bo15b3o98bo24bo5bo13b2o$2o8bo5bo7bo8bo98b3o23bo3bo$2o8bo3bob2o4bo bo135b2o$10bo5bo3b2o$11bo3bo4b2o$12b2o6b2o$22bobo7b2o$24bo7bobo$34bo$ 34b2o$129b2o$129b2o6$128b3o$105bo21b2ob2o$105b3o19b2ob2o$108bo18b5o$ 107b2o17b2o3b2o3$129b2o$127b5o$131bo$79bo47b3o$80bo46bo$73b2o3b3o29bo 17b2o$73b2o34b3o16b2o$108b5o8bo$107b2o3b2o6bobo$74bo33b5o7bobo5b2o3b2o $73bobo32bo3bo3b2o10bobobobo$72bo3bo10bo21bobo4b2o2b2o7b5o$72b5o8bobo 22bo10b2o7b3o$71b2o3b2o8b2o10bo23bo8bo$72b5o19b3o$73b3o19bo14b2o$74bo 20b2o13b2o2$128bo4b2o$126bobo4bo$73bo53b2o5b3o$61b2o12b2o16bo42bo$61b 2o11b3o15b3o$74b2o16b3o$75bo79b2o$74bobo13b2o3b2o38bo19b2o$60b3o12b2o 13b2o3b2o39bo$60b3o71b3o$59bo3bo91b3o$58bo5bo4b2obob2o10b2o5bo61b3o$ 59bo3bo22b2o4bobo$60b3o6bo5bo6bo11b2o$83b2o9b2o$70b2ob2o7b2o9b3o4bo52b 2o3b2o$72bo19bobo3b2o54b5o$92b2o5b2o54b3o$59bobo94bo$59bo2bo6b2o$61b2o bo5bo19b2o$67b3o$61bo5bo22bo2bo$61bob2o$62bo29b2o$155bo$95b2o56b2o$56b 2o3b2o32bobo56b2o$57b5o35bo$57b2ob2o35b2o$57b2ob2o23bo$58b3o22b2o$84b 2o69b2o3b2o$146bobo8b3o$146b2o8bo3bo$147bo9bobo$158bo$59b2o$59b2o2$ 157b2o$157b2o3$77b2o6bo$77bobo3bobo$78b3o3b2o$79b2o$79b2o$77bobo$78bo$ 92bo$93bo8bo$75b2o3b2o9b3o6b3o$39b2o34b2o3b2o17bo$39b2o58b2o$77b3o$77b 3o$78bo18bo$96bobo$65b2o24bo3bo3bo$64bo2bo21b2o5b3o$64bo25b2o2b2o3b2o$ 64bo51bobo$38b3o23bobo13bo35b2o$37bo3bo22bobo14b2o34bo$36bo5bo22bo14b 2o$36bo5bo$39bo6bobo26b3o12b2o$37bo3bo4b2o14b2o3b2o5bo3bo11b2o$38b3o6b o14bo5bo4bo5bo30bo$39bo33bo5bo28b2o$63bo3bo8bo10bobo19b2o$64b3o7bo3bo 9b2o6b2o$36b3o38bo10bo7b2o$36b3o34bo2bo$35bo3bo33bo$74bo$34b2o3b2o30b 3o27bobo$71bo23bo5b2o$68bo27b2o4bo$66bobo26b2o$67b2o2$51bo11bo$52b2o8b 3o$51b2o8b5o$60b2o3b2o36b2o$37b2o22b5o37bobo$37b2o22bo3bo39bo$62bobo 40b2o$63b3o$58bobo4b2o$59b2o4bo$59bo6b3o$68bo4$66bo$67b2o$66b2o6$84bo$ 82b3o$81bo$81b2o3$79bo$78b3o$77bo3bo$76bob3obo$77b5o11$78b2o$78b2o! *p30 signal splitters can be made with a gosper glider gun inline inverter and a reflect reaction that turns the input 90 degrees* x = 332, y = 319, rule = B3/S23 2bo$obo$b2o5$9bo$10bo$8b3o6$17bo$15bobo$16b2o5$24bo$25bo$23b3o6$32bo$ 30bobo$31b2o5$39bo$40bo$38b3o6$47bo$45bobo$46b2o5$54bo$55bo$53b3o6$62b o$60bobo$61b2o5$69bo$70bo$68b3o6$77bo$75bobo$76b2o5$84bo$85bo$83b3o6$ 92bo$90bobo$91b2o5$99bo$100bo$98b3o6$107bo$105bobo$106b2o5$114bo$115bo $113b3o6$122bo$120bobo$121b2o5$129bo$130bo$128b3o6$137bo$135bobo$136b 2o5$144bo$145bo$143b3o6$152bo$150bobo$151b2o5$159bo$160bo$158b3o6$167b o$165bobo$166b2o5$174bo$175bo$173b3o6$182bo$180bobo$181b2o5$189bo$190b o$188b3o6$197bo$195bobo$196b2o5$204bo$205bo$203b3o6$212bo$210bobo$211b 2o5$219bo$220bo$218b3o6$227bo$225bobo$226b2o5$234bo$235bo$233b3o6$242b o$240bobo$241b2o5$249bo$250bo$248b3o6$257bo$255bobo$256b2o5$264bo$265b o$263b3o6$272bo$270bobo$271b2o53b2o$326b2o4$279bo$280bo$278b3o3$323b2o bob2o2$323bo5bo$287bo$285bobo36b2ob2o$286b2o38bo3$320b2o6bo$319bobo5bo bo$294bo26bo4bo3bo$295bo30b5o$293b3o29b2o3b2o$326b5o$327b3o$328bo$306b 2o4b3o$306b2o6bo$313bo5$305b2o$304bobo21b2o$306bo21b2o$295bo$294b4o$ 293b2obobo6bobo$282b2o8b3obo2bo3bo3bo$282b2o9b2obobo4bo$294b4o4bo4bo$ 295bo7bo$303bo3bo6b2o$305bobo6bobo$316bo$316b2o!
Fishi's 3 anos atrás
I think building Calculators in the game of life will be much more difficult and time intensive than building it in minecraft :D
Belial Iscariot
Belial Iscariot 10 meses atrás
Nope. Or gates form the basis for many gates, some of which are impossible without it. Even the and gate requires or (technically). If you let a | b represent "a or b" and a & b represent "a and b" and !a represent "not a" (invert a), then the equation for and Gate is: a & b = !(!a | !b) so and gates and all other gates require an Or gate. The "or" gates and "and" gates in Life operate under a slightly different principle. Notice how the "output" is left or right. So there are two outputs makin it bidirectional logic... or by extension, Vector Logic. Thus, the "or" gate and "and" gate function a little more different with a little bit more complex mathematics.
Belial Iscariot
Belial Iscariot 10 meses atrás
XOR's are easy... have you built a computer yet in mc?
Multorum Unum
Multorum Unum Anos atrás
The pain is XOR gates
Random Guy
Random Guy Anos atrás
aren't OR Gates kind of useless, they're just a line of Redstone (with repeaters to stop back flow)
Redstoneboi 2 anos atrás
100% true redstone and torches on blocks are enough to make OR gates and NOT gates
Weebish Tomato
Weebish Tomato 3 anos atrás
Ok... Now try to make calculator with this :D
Belial Iscariot
Belial Iscariot 10 meses atrás
People have, including making the game of life in the game of life. Look it up. "Life in life". It's pretty neat actually. Very inspirational however he uses a slightly different approach then general mathematic logic.
Enlightened Groyper
Enlightened Groyper 3 anos atrás
Tygr Asijsky people have, im sure
Tyzoid 3 anos atrás
Cool, though FYI, you only need two gate combinations to make all gates: and+not / or+not. OR can be made by (not ((not A) and (not B))), and similarly, NOT and OR can be combined together to form AND, NOR, XOR, etc. Even better if you have NOR, as every gate can be made as a combination of NOR gates.
Belial Iscariot
Belial Iscariot 10 meses atrás
You only need or, not. No need for and because and can be defined by ors and nots.
Joe Dempsey, Sr.
Joe Dempsey, Sr. Anos atrás
NAME gates are generally used as the universal gate.
Michael Steshenko
Michael Steshenko Anos atrás
see video course / book nand to tetris
spaceshipable 3 anos atrás
Im pretty sure all commercial processors use NAND logic. The reason we use them over other universal gates is that they're very simple to make and they're very low power.
Appable 3 anos atrás
NAND has never actually been used in a computer architecture, though. However, Apollo's guidance computer used exclusively NOR logic gates.
Bryan Chu
Bryan Chu 3 anos atrás
I'm going to try making an adder
Michele Pugno
Michele Pugno 24 dias atrás
u cray man :D
This World And Beyond
This World And Beyond 4 meses atrás
@Prashant Batule Importing the python language and libraries into conway's game of life.
NetRolller3D 2 anos atrás
Dan Kelly Of course, it was a pun.
Dan Kelly
Dan Kelly 2 anos atrás
NetRolller3D Do you what an adder is, (in digital theory without having looked it up after you made your comment)?
NetRolller3D 2 anos atrás
Prashant Batule The scripting language Python. Also, "adder" and "python" are both snakes.
KeinNiemand 3 anos atrás
If logic gates are possible in conways game of life computers are also possible (I think)
Racon Vid
Racon Vid 2 meses atrás
FatMemeBoy people have made GOL in GOL.
Racon Vid
Racon Vid 2 meses atrás
People have made computers with it.
FatMemeBoy 3 meses atrás
Game of life in game of life in game of life in game of life
Niels Leest
Niels Leest Anos atrás
Someone made a digital clock...
Viktor Engelmann
Viktor Engelmann Anos atrás
Yes, implementing game of life in game of life is possible. See
Miraç Göksu Öztürk
good work, thank you
ff_____ 4 anos atrás
froakentoken 4 anos atrás
@Alex Bellos message is my real email address,my fake email address is so to prevent a permanate spam bot from getting into my email) if i were born with the mental difference of getting hurt touching unsmoothly shaped things (my clothes literally hurt my body 100% of the time,1/10 billion chance to be born that way when only 7.1 billion people in the world,supposed to search for inventing this for all people in the world) and im supposed to have its mental difference think up of the idea that it takes a letters that stand for something mathematical equation (example:e=mc squared) to invent a machine generating brainwaves that travel like electricity to go inside the person by touching the outside of the person (itll go onto the brain,and everwhere inside and outside of the person) and then the over 7 billion people out there that have a 100 year (36500 days) life span have a minimum of at least 1/36500 of themselves be killed of old age heart attack per day,and i think some super natural forces of unlikelyhoodedness tried to get me with grigory yakovlevich perelman,whom solved a 100 year old letters that stand for something mathematical equation with one milion dollars behind answering it (poincare conjecture) proving himself good enough to invent those brainwaves that travel like electricity,so any type of brainwaves possible to be programmed into it:regeneration similar to the hydra type of jellyfish where as the hydra type of jellyfish has an infinite life span and so would anyone whom wears such a machine'll have an infinite life span also,then it might be possible to program happiness the opposite of mental illness to undo gradual more mental illness with an infinite maximum mental illness for years or decades,or program pleasure (tons of happiness/pleasure) to feel really good 100% of the time,it might be possible to program in having the advantages of birth defects without there disadvantages,and get rid of disadvantages for people born that way so no more get hurt touching unsmooth/retarded,so get hurt touching unsmooth/retarded (retarded=so less intelligent/less capable that you cant speak or understand one word in your whole life timequite frankly getting hurt touching unsmooth only a small amount of retarded in comparison,a little bit less intelligent/less capable) *advantages without disadvantages of TONS of mental illness paired with getting hurt touching unsmooth's advantages is what makes you think up of how to invent it,so advantages of being depressed without being depressed is one more important type of brainwave (so,it either transmits to the brain,or modifys the brain with touching the person on the outside of the person,it working touching on the outside of the person means no operation to input inside of the person) *possible to pick up thoughts that flow a small distance away from the person,then you can read peoples minds,it might *possible to make you more intelligent/capable,or become psychic yourself *could be possible to go into a dream like stasis,then everything you imagine while awake is like as good as a dream,all kinds of modes here *so i think the super natural forces of unlikelyhoodedness are trying to get me whom get hurt touching unsmooth together with the grigory yakovlevich perelman person as i found him looking the same as me,then his three friends looking the same as my 1st/2nd/3rd period teachers in 6th grade in april 16 2014 grigory perelman said: Concerning Your Idea of Electronic Waves to Obtain Infinite Life. Dear Mr. or Mrs. Froakentoken3, I was contacted by several authorities and colleagues via email that you had done research into obtaining infinite life via electric waves. I would very much like to discuss these ideas with you, should you care to reply to my message. Sincerely, Григорий Яковлевич Перельман (Gregorie Yakovlevich Perelman) Sent to: froakentoken3 copy and paste and go into the website link: *so anywhom,thats the only thing he said,he cant say another thing no matter how many times i ask if he can tell me how long until the first of brainwaves that travel like electricity machines be invented,also cant tell me if he can hire a psychic to read his future:looking 10 years into the future for what letters that stand for something mathematical equation like e=mc squared hes gonna make,then have him know it right now,here lies where real psychics that the proof of police not know where/not knowing who to arrest until they called a psychic to locate who/where to arrest thus proof of real psychics and not frauds,and theyll really read your future or locate someone or (them being arrested when police couldnt find them without a psychic means that certain specific psychics not a scam,they really have psychic abilitys) so about 100 messages of these two questions and grigory perelman just didnt say anything: 1. how long until the 1st of brainwaves that travel like electricity machine is invented?? 2. can you have a psychic read your future to go about amillion times faster in inventing that brainwaves that travel like electricity machine? *so in his message when i asked him to make a new youtube account and contact froakentoken3,he spoke english even though russian living in sweden as of recently if you want to copy+paste it into web address bar url and go *this might seem strange,but can you (somehow) get into contact with him and message me what he says when you ask him questions 1. and 2. ? (whether you hire a psychic to the actual mathematician grigory yakovlevich perelmans phone number and write it down while still on the phone with a psychic so you wont forget with a pen/paper before you even call the psychic,phone book for his number,or find it without those ways,just somehow find contact with him,maybe you can do the standard hospital procedure to find where someone lives to call there family to pick them up from the hospital and find grigory yakovlevich perelman that way and call him for this even though its not to have him pick someone up from the hospital) *then report how long/whether or not he can hire a psychic to read 10 years into the future for all things he wouldve done,then do them now (have him write down with a pen/paper in hand before he even begins calling them and have him write down using that what he wouldve done while still on the phone with a psychic,so he doesnt forget and need to hire/ask a psychic again)
MadEngineer 3 anos atrás
I have grokked the meaning of life after reading this. :)
k3wlk1d 3 anos atrás
bl_ash 5 anos atrás
Very informative! Thanks!
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