Cambridge has a new mathsy train station

[@JaccovanSchaik]

Some PR person probably heard it explained as "a bit like Conway's Game of Life" and thought "oh I've vaguely heard of that", and so it stuck.

[@MrCheeze]

These 1-dimensional games of life were directly inspired by Conway's game, so it's​ really not very far off.

[@user93237]

It could actually be rule 135 run in Conway's Game of Life. You'd need to subsample the grid to hide the additional structure though.

[@TheGrooseIsLoose]

okorok Even better: it's rule 135 run in Conway's Game of Life. This is the initial state.

[@lizardbaron3727]

"Take that Oxford"

[@gazman237]

Lizard Baron Oxford parkway :P

[@jacksainthill8974]

Penrose tiling, take that Cambridge.

[@thesonofasniper]

Bicester has three now

[@DeGuerre]

Fun fact: Storey Hall at RMIT in Melbourne (Australia) is designed with Penrose tiles. I'm not sure what this has to do with RMIT.

[@pierreabbat6157]

Doesn't that make it Tricester?

[@seanm7445]

Seems like a Parker Square of an architecture project.

[@danielleahearn8714]

Sean M critiquing some abstract art are you?😋

[@seanm7445]

Oh hai there. Always nice to meet people outside of Facts. channel :D

[@ceafdc]

0:20 "John Conway `is` a british mathematician" John Conway is still alive

[@pegy6384]

Is he still an active mathematician? If he's retired, that would explain that he 'was' a mathematician.

[@KiloOscarZulu]

Yes, I also noticed that and I had to check to make sure that he is still alive.

[@eduardomezencio4057]

As soon as I heard John Conway WAS, I paused the video and went in a hurry to wikipedia to see what happened... I'm glad it's nothing

[@pegy6384]

You can certainly quit getting paid for being a mathematician. I suppose in that way it's like being a musician--you keep playing whether or not anyone is listening.

[@patricksheldon5859]

Is he still British?

[@cherrytaly9765]

finally a new video by u ...been waiting for it for months! I know u must be busy bt plz keep posting videos ...I just love them!!😍

[@sebastianespejoloyaga7603]

cherry taly *for months

[@cherrytaly9765]

Sebastián Espejo Loyaga ...okay bro?

[@uofmrob]

Agreed!!!

[@mikekuppen6256]

+

[@Lightn0x]

"John Conway was a British mathematician". That "was" made me google if the poor fella died.

[@UnderscoreZeroLP]

woo, semantic ambiguity

[@benwilcox1192]

:(

[@PeterAuto1]

Sadly he died because of corona

[@VincentZalzal]

Interesting, I had never heard of this rule! For those who prefer to remember the rule using logic: if you name the pixels A, B and C, then the rule is A XOR (B OR C) (where white pixels are true), if I am not mistaken.

[@jonlottgaming]

I don't think thats right. If labeling CBA from left to right, I get ((A NAND B) AND (NOT C)) OR (A AND B AND C) although they might be equivalent

[@kaychimav]

010 also becomes 1. Also, 110 and 011 are symmetric, but their output is not the same, while the equivalent is not true for 001 and 100.

[@VincentZalzal]

@jonlottgaming I've worked out your version, and it is also correct. You labeled the pixels in the opposite order I used, and you considered black as true, whereas I considered white as true.

[@jonlottgaming]

Ah ok, that makes more sense! I said black was 1 as the output at the bottom is black when the 1 is underneath at 1:29.

[@VincentZalzal]

Indeed. If we want it to be called rule 135, it has to be black == 1 :) Where I work, I am used to white being 1, that's all. With your labeling CBA, and black == 1, it can be further simplified to (A AND B) XNOR C, or (A && B) == C, if you prefer.

[@connorp3030]

Can you explain how rule 110 can be used to simulate computer programs or do calculations?

[@tjejojyj]

connorp3030 yes. My question as well. I presume it's because the rules effectively reflect logic operators - AND, OR, NAND etc.

[@Puj0]

connorp3030 If you are impatient you could search for book New Kind of Science by Stephen Wolfram. If I recall correctly there is explained why rule 110 is Turing complete, ie. why it could be used as a computer (very impractical one).

[@ThatGuy-nv2wo]

Yep, rules can be used as logic gates, so you can create a basic RISC. Completely impractical, as Pavle said, but could be fun to make a compiler/interpreter for (I might just try that).

[@Great.Milenko]

That Guy nice profile pic 😀

[@columbus8myhw]

From Wikipedia: "[Matthew] Cook proved that Rule 110 was universal (or Turing complete) by showing it was possible to use the rule to emulate another computational model, the cyclic tag system, which is known to be universal. He first isolated a number of spaceships, self-perpetuating localized patterns, that could be constructed on an infinitely repeating pattern in a Rule 110 universe. He then devised a way for combinations of these structures to interact in a manner that could be exploited for computation." Source: en.wikipedia.org/wiki/Rule_110 It provides the following links: en.wikipedia.org/wiki/Turing_complete en.wikipedia.org/wiki/Tag_system en.wikipedia.org/wiki/Spaceship_(CA)

[@dhmdm3106]

Glad to see a new video from you. It's those little things that keep me motivated to learn new things I would never have found by myself :-)

[@Innovativemagi]

I love the coincidence of finding this channel twice; once through mismag822 and mathemagic and the second through Brady's videos on numberphile. I wonder how many other people can site two unique means of discovery to this channel.

[@Liliou]

So happy to enjoy a new video of Mr Grime! And something interesting I didn't know about, and that I'm going to have fun researching and learning about! :D Thanks for sharing!

[@Hauketal]

Great to see you again. And in the same KZbin proposals list a video by Geoff&Vicky aka All The Stations.

[@domramsey]

The difference between Cambridge and Oxford is that Oxford mathematicians can count to two. Oxford, Oxford Parkway. :p

[@uh6679]

Jake Staines It is a London airport; it's just not an airport in London

[@uh6679]

*****​ Shit, i am unbelievably stupid

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@pierreabbat6157]

Oxford, Oxford Parkway, Oxford Oxford, Oxford Parkway Parkway, Oxford Parkway Oxford, ...

[@DuncanBooth]

+Eddard Stark As indeed is Oxford Airport, or to give it it's full name, London Oxford Airport. Take that Cambridge with your puny Cambridge International Airport! (What is it with these dumb airport names?)

[@elliottmcollins]

I am always excited to see you've posted. Off to make a bunch of rule-based graphs!

[@MartiniComedian]

I'm just happy to see that you're alive! ;) Please post more videos!!!

[@senc1971]

Good to see a new video on your channel, but I'm glad that there are now several months between videos--easier to keep up with that way. It's a good thing you aren't letting commenters pressure you into uploading more often, as the quality would almost surely decrease and people would end up taking them for granted, like those numberphile videos that come out all the time....

[@singingbanana]

Your sarcastic comment won't help.

[@senc1971]

Sorry, wasn't meant to be obnoxious. I really do get overwhelmed with keeping up with certain things at times. I realize that this isn't your job and I'm grateful for all the videos you've made, as I said in an earlier comment (Fancy Dance 2009).

[@singingbanana]

+senc1971 Then I am sorry!

[@ivanvojvodic8350]

Yay!!!!! James is not dead!!!!!! I look forward to more videos

[@UMosNyu]

I am having problems around the edges. If I asume that we have an infinite array of 0 and then somewhere our starting sequence, rule 135 (and any rule with 0 0 0 -> 1) turns the whole infinite region into 1. So my questionwould be: what to do at the edge? loop around and take the last element?

[@omkelderman]

on 1:22 there is the explanation of the rule, but one part I dont get is the cells at the begin and end of the line: They lack a neighbour, and I cant seem to be able to figure out the logic used there to produce the next line, since if you take the left most cell of the first line, its black, with a black cell to the right, but below its black as well. That means that according to the rules there must be a black cell to left, so it doesnt "wrap around" since the right most cell if the first line is white. So do we just assume black at the edges?

[@jetison333]

depends on what you want really. you can assume black, or white, or wraparound.

[@omkelderman]

makes sense I guess :D

[@Dayumhesgood]

Sorry James, Oxford also has 2 train stations now: Oxford and Oxford parkway...and its second station opened before Cambridge north.

[@johnmasters504]

Cambridge North is actually in Chesterton not Cambridge

[@sardonicnerd]

Please. Oxford has had a second train station (Oxford Parkway) for quite some time.

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@miroslavkollar9577]

nice to see this channel still lives :)

[@leow_se]

Oxford has TWO railway stations. The new one opened in last 2015

[@Nanaki404]

I tend to prefer rule 150, partly because it is its own color-swap rule (unlike rules 30-135) and is also symmetric left-right. And I love how, starting with a random sequence, it produces black triangles and white triangles everywhere.

[@lsbrother]

Conway's Game can produce many different patterns depending on the initial configuration; is it inconceivable that it could produce Wolframs rule 135 pattern?

[@BertGrink]

That inserted sequence from the actual Game of Life, is that the Gosper Glider Gun?

[@XMegaJuni]

Your videos are fantastic. Please continue to share your awesomeness.

[@abdullahalarfaj4930]

Will periodic behavior be a result of a rule? or the combination of a rule and an initial state? a follow up video on the pattern required :)

[@IcyDiamondDust]

I lived in Cambridge, I yelled at you while running past the (old) station a few months ago! Good video :)

[@mathmusicminecraft]

AAAAA when were you in Cambridge??? I could have arrived at the station too!! if it was open?

[@Piineapple.]

However if you take a finite number of squares in a line like here, there will be a moment where you'll return on the initial configuration, so the model is condemned to repeat

[@jalexander9520]

How is the next row decided for the squares with one neighbor?

[@gustavagerbo3236]

Great to see you are uploading videos again!

[@Wiki7202]

anyone notice the autofocus in the background? phases in and out of focus frequentlly

[@error.418]

Eh, some cameras aren't as good at autofocus as others.

[@tonyjones9442]

This video came up in my feed. I saw a KZbin video on "all the stations" (Geoff Marshall) regarding this station, and they mentioned the patterns but didn't give much away. This video was good, but for the layman. It was a bit of a fast explanation. It's triggered my curiosity so will look into more. Good enthusiasm though!!

[@DesmondAltairEzio]

what about the squares on the edges? how is that determined?

[@TheDeetster]

oh man i would love to have seen him talk more about this like i wish it was a 30 minute video as opposed to 3

[@dipi71]

2:02 »randon, non-repeating nature«; what did the architect do with it? Make it repeat.

[@BhupinderSingh-xv6dk]

My man James you are a true soldier and true citizen . your service to community is priceless.

[@tedspeak]

Such an affable person and a pleasure to listen to! I was never good at maths but no matter! Thank you

[@danielthebingham]

I'd like to point out we have Oxford and Oxford Parkway as stations, so as usual Cambridge are playing catch up.

[@singingbanana]

+danielthebingham Are they mathsy train stations?

[@danielthebingham]

singingbanana sadly not

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@TimMeep]

On another site someone posting as "Quintin Doyle, Senior Architectural Designer, Atkins" says its Stephan Wolfram's Rule 30. They posted "What we liked most about rule 30 was it was as close as we could find to a 'random' non repeating pattern."

[@Tsanito]

How does the rule treat the edges? I can't seem to see the pattern.... or your graphic is misleading.

[@hugoharada5301]

How do I decide the color of the first square of the second line?

[@Dev1nci]

I see 2 problems with the concept firstly (as mentioned by others) they've repeated a formula famous for it's randomness and secondly parametric design is a much better way to generate architecture from maths. What that means is that if you use maths in this way it lacks a lot of depth that can be found in contemporary architecture to date. This facade can be compared to someone who puts E=MC² on their facade and saying that the facade was derived from quantum mechanics.

[@davidescobar6300]

you are here, oh my god. Thank you forma coming

[@gabest4]

If you use the average value in gray scale, that simulates a burning flame surprisingly well. Old demos used it all the time back in the last millennium.

[@error.418]

awesome! I would love to try this.

[@prestonjensen6172]

how do you find the color for the edge cells? they don't have the requisite three cells above them to determine their color

[@singingbanana]

Assume it's an infinite row of white cells.

[@prestonjensen6172]

That''s interesting, because the rows will alter between black and white, given the rule that three whites make a black.

[@stevethecatcouch6532]

+Preston Jensen In Rule 135, three blacks also make a black, so if you start with ... 0000000000001000000000000....., the next few rows will be ...0000000000001000000000000... ...1111111111111011111111111... ...1111111111110001111111111... ...1111111111100110111111111...

[@prestonjensen6172]

Oh, yes. You're right.

[@Dylan-ii1ds]

And now it is 3 years and 2 weeks old for those of you viewing this in June 2020

[@6_6740]

ok just tried to code it - what happens on the edges? the ones that only have one neighbour.. edit: it`s just two times the same

[@CBMaster2]

How do you apply the rule for the 2 corner pieces?

[@TheXatheron]

how can it be non periodic if there's only finitely many states?

[@AlRoderick]

Tom Anderson there's only ten possible digits yet pi is not periodic.

[@Tumbolisu]

It depends on how much room you got.

[@TheXatheron]

Alexander Roderick but unlike pi in this case given state of row X we can work out the state of row X+1 with certainty because of the way the rule is defined, each states only depends on the state above it, so when we repeat states the whole pattern should repeat as far as i understand. whereas with pi we can't say given a digit 5, the next digit must be 7, it's impossible to tell the next digit without knowing the full context

[@stevethecatcouch6532]

+Tom Anderson *"so when we repeat states the whole pattern should repeat"* In your comment, you used the term "state" to refer to the state of the automaton as a whole, i.e., the pattern. In effect, you are saying the pattern will repeat when the pattern repeats. Each cell has only 2 states and each 3 cell block has only 8 states, but there are infinitely many of each, so the automaton as a whole has potentially infinitely many states.

[@AlRoderick]

I think your confusion comes from the fact that the artwork is of fixed size, the rule with these games is that the hypothetical grid is infinite. Rule 135 makes the pattern explode off chaotically to the far corners of the universe so it's never back in any previous state again.

[@DISammi]

Waiting for a singingbanana video is the most exciting maths adventure on the internet. Do more puzzles they are fun!

[@livedandletdie]

Couldn't they had use Rule 255 or 0 because I like Black and White. 127 works too if we want grey. Although it's technically alternating black line white line black line white line...

[@romanski5811]

Endlich gibt es wieder Video von dir! Bitte mehr davon.

[@wyattstevens8574]

W30 is the B/W reversal of W135 shown here, so that could be an "almost valid" description!

[@Jean-Berry]

RIP John Conway

[@milogill-taylor9851]

do you still make videos for numberphile

[@DanDart]

i saw this on a video about animal shells and made a program to use any wolfram rule.

[@DesmondAltairEzio]

Messing around with this, rule 154 produces Sierpinski's Triangle if you input only one cell filled in! Neat.

[@error.418]

very neat!

[@anshulraman4503]

Same guy created wolfram alpha?

[@davidwuhrer6704]

Yes.

[@columbus8myhw]

In fact, the loading animation on Wolfram Alpha is also a cellular automaton (though more similar to Conway's Game of Life than to Rule 30): stackoverflow.com/questions/27332460/what-is-the-cellular-automaton-shown-as-loading-screen-on-wolfram-alpha

[@ClaskoTheKnight]

Why did the elaphelk cross the road?

[@withedoter6277]

Welcome back Master!!!

[@noterictalbott6102]

Great to see a new video!

[@bittertea]

Informative as always. Thanks for the video. It's been a while. Let your inner banana sing more often. :P Coincidently, I am programing Conway's Game of Life in C++. It's a lot of loops, like two arrays (but I think it's possible to do one only) and scanning user made functions. Pattern is a bit random looking and I don't know if it would translate well as a design. That wasn't the point though. The station was suppose to honor the work of scholars in the area but it didn't. Rule 135 or 30 done in Princeton, New Jersey. *Ouch.* John Horton Conway is still alive. I wonder if he will comment.

[@EllipticGeometry]

Hey, my favorite singing banana is still here. Nice stuff. I just feel like strangling the autofocus. It keeps tempting me with an almost-sharp image of the terminal and then jumps back to a total blur.

[@ekp8525]

The camera can not decide whether to focus on James or the subject of the video!

[@toastysauze]

There is a rule 30, 110, 135 I am genuinely curious as to if there is a rule 34, and what it is if so.

[@joinedupjon]

Stephan Wolfram who went to Oxford?

[@Kiwiscore]

he's back!

[@kaleyschuster1951]

Ahh I was just in Cambridge! I didn't know about this! Dammit

[@doctorbobstone]

If they had chosen rule 110 (or any other Turing complete rule) then they could at least *try* to save face by claiming that it was actually simulating Conway's Game of Life... And such a simulation is likely large enough that it either could be true or would at least be tricky to disprove. I admit it's not much of a dodge, but they could try...

[@jakeroosenbloom]

Wow this channel still exists...

[@alech8336]

? Train station? I only entered and left Oxford in my classic Maserati when I was a student there.

[@JudgeHill]

Of course, Oxford also has a second train station. As with many efforts, Oxford got there first!

[@ShadowDrakken]

Why reference a living person (Conway) as if he had passed on (was)? o_O

[@anon6514]

Welcome back!

[@hanniffydinn6019]

I got a shell with this pattern on yesterday ...as I knew it was this kind of pattern interaction....

[@ferncat1397]

That suspense before the 'thanks for watching' had me worried :P

[@shamrockfrost1856]

I'll definitely get around to implementing game of life... Tomorrow....

[@TheNgandrew]

Fascinating subject, and a fascinating video. Thank you.

[@flamencoprof]

Sounds just like the cellular automaton I programmed my C64 for in about 1984 after reading about it in Scientific American. It ran by directly manipulating the screen memory but Peeks & Pokes were too slow & I had to learn opcodes to make it go faster. It was fun tweaking the rules to find a sweet spot between totally random & boring repetition,

[@stumbling]

hmm I created this by accident when I was making a game of life program years ago. Had no idea it was its own thing.

[@joelcolyer2240]

Oxford and Oxford Parkway?

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@TheSingingNerd]

Fascinating as always!

[@iDEaXANA]

8 month upload schedule. noiiice!

[@junkfeed6188]

I thought you have done video posting. Please post more videos like before.

[@coryman125]

Now all we need is an "unpause simulation" button and the pattern will become that much more interesting! Unless of course it's a pattern that will eventually die off...

[@Nayson]

Oxford has got two railway stations too, Oxford and Oxford Parkway, so there. :P

[@singingbanana]

+RandomNameHere We're catching up

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@daysofsunshine5974]

mate... Oxford has 2 train stations as well

[@daysofsunshine5974]

since 2014/2015

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@oz_jones]

But they aren't mathsy. So, *take that, Oxford!*

[@sk8rdman]

Your camera is so confused about where to focus.

[@hannahhannon8877]

why does the government keep investing in inessential facilities for prosperous areas (the inner bouroughs of london e.g hackney, oxford and buckinghamshire) whilst places such as stoke-on-trent are suffering drastic budgeting cuts on childerns services.

[@Turcian]

Woah, it's been a while!

[@Nai61a]

"It's (a game of) life, Jim, but not as we know it." Star Trek related quotes - just occasionally they come in useful!

[@EderAlbertoContreras]

why did you write all in spanish? o.O

[@swinger9374]

Sorry but you just ignored Oxford Parkway station...

[@oz_jones]

Not in Oxford.

[@alinemsmenezes]

How did u find out its exactly rule 135?

[@alinemsmenezes]

Wolfram has done it himself... blog.stephenwolfram.com/2017/06/oh-my-gosh-its-covered-in-rule-30s/

[@RBXTrains]

Oxford has 2 train stations though?

[@error.418]

Technically Oxford Parkway is not in Oxford. It's in the hamlet of Water Eaton.

[@beeble2003]

Yeah, might want to do a bit more work on this one. In the first thirty seconds you suggest that John Conway is dead ("was a British mathematician") and that Oxford has only one railway station (it's had two since October 2015).

[@testaccount737]

beeble2003 also, Stephen Wolfram is a British mathematician, although his company is based in America

[@beeble2003]

Excellent point, though that mistake isn't in the first thirty seconds. ;-)

[@testaccount737]

true, still something that would have required a little more dedicated research ;)

[@darcipeeps22]

I don't understand 'Turing complete'

[@error.418]

en.wikipedia.org/wiki/Turing_completeness