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.
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'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.
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.
+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?)
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).
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).
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)
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.
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.
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!
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."
This video came up in my feed. I saw a RU-vid 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!!
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.
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?
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.
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....
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).
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...
The capacity of people to make those dumb mistakes never ceases to amaze me. It is in big budget movies, and other projects where it's really mind blowing. Did they not bother to ask a mathematician? Are the mathematicians employed by them just don't understand what they're doing? Surely it can't be that difficult to get it right.
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.
Conway's Game can produce many different patterns depending on the initial configuration; is it inconceivable that it could produce Wolframs rule 135 pattern?
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?
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.
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
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...
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,
Imagine a mathematical paradise where all 256 stations existed and mathematicians of a higher calibre lived in the more posh rule's suburbs and would sneer at those less capable who had to live in the more boring districts. Imagine rolling into Rachel Riley's "district"?
I knew immediately that this was Wolfram, not Conway. That makes me a geek! However, I didn't know which pattern number it was, so I just missed qualifying as a nerd :(
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...
Conways game of life being turning-complete means you can simulate conways game of life inside conways game of life. It has been done, i have a copy of it, it works.
