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Oh My Gosh, It’s Covered in Rule 30s (stephenwolfram.com)
703 points by seszett on June 2, 2017 | hide | past | web | favorite | 149 comments



James Grime (of, perhaps, Numberphile fame) made a video about it [1].

He also talks about how it's supposed to be related to Conway's game of life but is actually not (Conway's game of life is a 2D cellular automaton, while rule 30 is 1D).

[1]: https://youtu.be/aeyhnrZvQBE


Rule 30 is 1D? Could you please elaborate on what you mean?


The pictures you're looking at, one of the axes is time. One row "becomes" the row below it. Each time-step iteration adds a row to the bottom, while the rows above it are immutable (because they are in the past).


This leads to the natural follow-up question:

You can take a 2D automaton like Conway's Game of Life and turn time into a third dimension, giving you a single static volume. Has anyone tried doing that and 3D printing it?


I found https://www.wired.com/2014/10/3-d-printed-shoes-generated-us... which seems cool

Perhaps easier than 3D printing would be stacked laser-cut acrylic sheets. You could use transparent and partially opaque colors for dead and live cells, which lets you see the interior 3D structures more clearly than purely opaque 3D printed structures. I think the optical quality would likely be a lot better than anything I've seen 3d printed.

I'm interested enough in this idea to see if I can come up with some interesting figures to make.


Would be very cool. Even just an LED Matrix that showed the game of life in 3D (time being the upwards/vertical step) would be cool


have you thought about this? it would fall apart.


The walls along 101 through a stretch of Menlo Park have error diffusion dither patterns on them that I enjoy. Or at least it looks like an error diffusion dither and not a cellular automata to me, because it seems like a gradient, somewhat random, sparse, spread out, and not deterministic enough to be a cellular automata rule.

https://www.google.nl/maps/place/Menlo+Park,+CA,+USA/@37.586...

Here's a few layers of cellular automata (anneal, life and brian) combined with some error diffusion dithered heat flow, for your enjoyment (try clicking and dragging and spinning the mouse wheel):

http://donhopkins.com/home/CAM6/


What exactly is going on in the second link?



Sweet, thanks. Without digging up the book, am I reading this right that this isn't a memoized algorithm like Hashlife, it's just that Javascript got that stupidly fast?


JavaScript got unexpectedly inconceivably stupidly fast. That code is not at all optimized (except that it tries to use efficient algorithms), and is very data driven and dynamically parametrizable with dictionaries, yet somehow it still runs really fast! JavaScript optimization is the new moon shot.

It can emulate the CAM6 hardware, which uses look-up tables pre-computed from FORTH (now JavaScript) functions, which don't need to be optimized because they're run once over all possible inputs to generate the table, instead of for every cell of every frame.

The trade-offs of hardware and software have changed a lot, and it's more than fast enough, so I optimized for readability and flexibility. It can run CAM6-compatible (but limited) lookup table based rules (for von Neumann, Moore and Margolus neighborhoods), and also run arbitrarily complex and multi-layered rules in JavaScript, that compute the cell value directly.

https://en.wikipedia.org/wiki/Von_Neumann_neighborhood

https://en.wikipedia.org/wiki/Moore_neighborhood

https://en.wikipedia.org/wiki/Block_cellular_automaton

The rules can be parameterized by dictionaries (including stuff like like simple numeric parameters, or arrays of convolution kernels, or additional lookup tables) that you can tweak while it's running.

(The CAM6 lookup table isn't related to hashlife -- it's simply indexed by concatenating all the bits of the neighborhood together to make a binary number indexing into the table of next states -- that's what the CAM6 hardware did directly at 60 frames a second, on a 256x256 matrix, of 8 bits per cell.)

https://en.wikipedia.org/wiki/Cam-6

CAM-6 Forth source code:

http://www.donhopkins.com/home/code/tomt-cam-forth-scr.txt

http://www.donhopkins.com/home/code/tomt-users-forth-scr.txt

Rudy Rucker writes about his CAM-6 in the CelLab manual:

http://www.fourmilab.ch/cellab/manual/chap5.html

Computer science is still so new that many of the people at the cutting edge have come from other fields. Though Toffoli holds degrees in physics and computer science, Bennett's Ph.D. is in physical chemistry. And twenty-nine year old Margolus is still a graduate student in physics, his dissertation delayed by the work of inventing, with Toffoli, the CAM-6 Cellular Automaton Machine.

After watching the CAM in operation at Margolus's office, I am sure the thing will be a hit. Just as the Moog synthesizer changed the sound of music, cellular automata will change the look of video.

I tell this to Toffoli and Margolus, and they look unconcerned. What they care most deeply about is science, about Edward Fredkin's vision of explaining the world in terms of cellular automata and information mechanics. Margolus talks about computer hackers, and how a successful program is called “a good hack.” As the unbelievably bizarre cellular automata images flash by on his screen, Margolus leans back in his chair and smiles slyly. And then he tells me his conception of the world we live in.

“The universe is a good hack.”

[...]

Margolus and Toffoli's CAM-6 board was finally coming into production around then, and I got the Department to order one. The company making the boards was Systems Concepts of San Francisco; I think they cost $1500. We put our order in, and I started phoning Systems Concepts up and asking them when I was going to get my board. By then I'd gotten a copy of Margolus and Toffoli's book, Cellular Automata Machines, and I was itching to start playing with the board. And still it didn't come. Finally I told System Concepts that SJSU was going to have to cancel the purchase order. The next week they sent the board. By now it was August, 1987.

The packaging of the board was kind of incredible. It came naked, all by itself, in a plastic bag in a small box of styrofoam peanuts. No cables, no software, no documentation. Just a three inch by twelve inch rectangle of plastic—actually two rectangles one on top of the other—completely covered with computer chips. There were two sockets at one end. I called Systems Concepts again, and they sent me a few pages of documentation. You were supposed to put a cable running your graphics card's output into the CAM-6 board, and then plug your monitor cable into the CAM-6's other socket. No, Systems Concepts didn't have any cables, they were waiting for a special kind of cable from Asia. So Steve Ware, one of the SJSU Math&CS Department techs, made me a cable. All I needed then was the software to drive the board, and as soon as I phoned Toffoli he sent me a copy.

Starting to write programs for the CAM-6 took a little bit of time because the language it uses is Forth. This is an offbeat computer language that uses reverse Polish notation. Once you get used to it, Forth is very clean and nice, but it makes you worry about things you shouldn't really have to worry about. But, hey, if I needed to know Forth to see cellular automata, then by God I'd know Forth. I picked it up fast and spent the next four or five months hacking the CAM-6.

The big turning point came in October, when I was invited to Hackers 3.0, the 1987 edition of the great annual Hackers' conference held at a camp near Saratoga, CA. I got invited thanks to James Blinn, a graphics wizard who also happens to be a fan of my science fiction books. As a relative novice to computing, I felt a little diffident showing up at Hackers, but everyone there was really nice. It was like, “Come on in! The more the merrier! We're having fun, yeeeeee-haw!”

I brought my AT along with the CAM-6 in it, and did demos all night long. People were blown away by the images, though not too many of them sounded like they were ready to a) cough up $1500, b) beg Systems Concepts for delivery, and c) learn Forth in order to use a CAM-6 themselves. A bunch of the hackers made me take the board out of my computer and let them look at it. Not knowing too much about hardware, I'd imagined all along that the CAM-6 had some special processors on it. But the hackers informed me that all it really had was a few latches and a lot of fast RAM memory chips.


Fascinating. It makes it sound like the board had... video input/passthrough of some sort?


I think I remember that was in the book, that you could configure it to include video input in the CA neighborhood.

DonHopkins, great work! I wrote a JS engine inspired by the same book too, not so fancy: https://github.com/darius/js-playground/blob/master/ca.js but you can edit JS code live to change the rules and such: http://wry.me/hacking/ca.html I should make it use fatter pixels like you did.


The only sad part of this story is the design was meant to celebrate John Conway and his Game of Life [1] (Conway actually was a lecturer at Cambridge, when he introduced GoL).

[1] From 2014: http://www.railwaygazette.com/news/infrastructure/single-vie...


cladding which is derived from John Horton Conway's 'Game of Life'

Strange that no one was there to tell them they are wrong. Anyway, how could they get it wrong in the age of Internet? Every bit of information about 'Game of Life' is one click away... :( Agree - that's sad...


I went to school with architects of the aesthetic variety (vs. the keep your family dry with a good roof variety).

1. To their way of thinking, what we think of as "superclasses" are more like classes to them. i.e. They see little difference between GoL and Rule 30. They are essentially the same to them. The aesthetics are similar and the process is similar. Most importantly, the intention or thought process which produced the technique is almost identical.

I like the example below about Eliot vs. Shakespeare, although it's a bit overblown. I don't think architects would go so far as to conflate an entire museum to the entire works of two different individual's lives, especially when the two had such differing approaches to playwrighting. YET, conflating variants of two individuals' algorithms is within their scope, clumsy as it is.

2. Furthermore, architecture is an unclean collusion of politics, aesthetics and technique. It's very difficult for all three of these parties to have the same vision. Errors get amplified. White lies persist to save feelings, face and budgets.

3. In conclusion, yes they are wrong and intellectually lazy, and emotionally fearful about making it right. That brings me to my last point about architecture: Once it's erected, it's generally there to stay, baby. A bird in the hand. This is why architecture is so valuable to politicians. On three fronts: it's protection in the form of walls. It's production in the form of moving people where they need to go. It's influence in the form of symbolic power which will dominate the thinking of all those who pass through those walls. For many years. Who can argue against the triumph of digital patterns in shaping our generation?

Even though we're right, we're right like Big Bang Theory characters. No one wants to agree with us, because we're subordinate to the power of architecture (as leveraged by state politics). Our objections are a cute footnote on a museum tour for your aunt to amaze you with on a holiday weekend :)


Very nicely said! I really enjoyed your comment :)


That's because this is, like a commentator below said, a mix of aesthetics, politics, and technique.

As an architect and software developer I will bet my hat that the architects knew exactly what was going on, but said that it was based on the GoL precisely because it would pass the budget.

I wouldn't be surprised if it started out with the GoL, but, thanks to budget reasons, they were forced to fabricate multiple identical panels rather than a total unique facade, and switched to a CA.

Fabricating/plasma cutting such a facade would be hugely pricey and the only thing that would let it survive against a bottom line budget is a political reason - aka a talking point.


waterjet, probably, and I don't think it would be too pricey since you can stack many sheets.


Good call, But pricey than the alternative, which is to not cut a pattern at all, or to cut a unique pattern. Also, at this kind of scale, people easily balk at a reasonable sum; if it costs, say, $100 to waterjet one 4'x8' sheet, then a facade at 20'x40' on 4 sides of a building is all of a sudden a $320k budget.


May be they consulted with Stephen Wolfram.


Do you really, really, really think the architects didn't do their homework? Can you think of no other possible explanation they went with rule 30 and not GoL?


Like what?

They decided meanwhile that they would like to celebrate Wolfram instead?

Or is there any artistic value to celebrate someone with other persons achievements? Some kind of twisted post-modern artistic message about authorship?

Or it looks better for them? For example: lets pay tribute to Amundsen reaching the South pole with polar bear images (because they are so cute)?

By Occam razor: ignorance is the best explanation. ;)


Maybe they tested both and found one more aesthetically pleasing?

Maybe Game of Life simply doesn't produce patterns as interesting as Rule 30? With GoL you can only show one generation.

Maybe they were going for the randomness that rule 30 provides (you can build a PRNG from it) but Game of Life doesn't?

http://aperiodical.com/2017/05/right-answer-for-the-wrong-re...

They're professionals like you. Give them some credit.


Ok. So they are not ignorant or stupid, but have a twisted value system?

Imagine that you go to a Shakespeare festival but they only recite T. S. Eliot. When you are disappointed, they say:

"Look these are all poems. They are very similar on the surface, but Eliot somehow sounds better to the modern ear. Long live Shakespeare!"


No, they got the order to make something that looks like GoL.

They tried it out, realized it didn't look great, then looked for what most people who don't have a CS degree would consider similar enough and also looked nice.

This sort of reasonable compromise happens all the time. In the software industry, if you picked ideological purity over pragmatism you wouldn't be a great engineer.

You may have a point if this was a museum celebrating Conway, but it isn't.


Pragmatic choices one can forgive, but that doesn't make it right to pretend that a thing is something it isn't. Ultimately, it seems someone there is simply lying to people.

And you may think it's trivial, but it's exactly how - step by step, creative decision by creative decision - we turn each other into idiots with little clue about how reality works. Something that was discussed at length just few hours ago:

https://news.ycombinator.com/item?id=14460013

See also: http://tvtropes.org/pmwiki/pmwiki.php/Main/TheCoconutEffect.

I strongly second the quote that I once found on the Internet: "Promoting less than maximally accurate beliefs is an act of sabotage. Don’t do it to anyone unless you’d also slash their tires".


(I'm not a lawyer, only a layman.)

> "Promoting less than maximally accurate beliefs is an act of sabotage. Don’t do it to anyone unless you’d also slash their tires"

Regardless of whether the first sentence is accurate (and indeed it certainly seems accurate), I believe the prescription given in the second sentence is not entirely accurate.

Slashing someone's tires is absolutely/always illegal (property damage, or whatever the term is for causing it) ... whereas sabotaging someone's beliefs is illegal iff the "someone" is a court of law or government official, or if the belief-being-sabotaged is about a living person such that a falsehood constitutes slander.

As such, sabotage of beliefs is possible in some cases where tire-slashing is not.


When did "legally can" and "should" become equivalent? I don't mean to focus on this particular instance of using them interchangeably; I feel like Reagan gave an executive order that I missed.


> When did "legally can" and "should" become equivalent?

They didn't; e.g. playing the lottery as an adult is both legal and insanely idiotic. (Don't misunderstand me; I do like it that the insanely idiotic are able to self-select themselves away from their money with such ease.)

But on the other hand, "legally can and causes more utility gain per unit time than any other course of action" ... does indeed imply "should".

(And unless you're really silly, "utility gain" simplifies to "monetary gain".)

Of course, I'm not trying to imply that sabotage-of-beliefs is that powerful an action; indeed, my ultimate conclusion is that neither tire-slashing nor sabotage-of-beliefs present a compelling benefit-per-cost.


> And unless you're really silly, "utility gain" simplifies to "monetary gain".

Yeah, that's why I always turn down my friends when they ask if I want to go see a movie. Monetarily, it's nothing but a loss, and I would have to be "really silly" to value an entertaining experience.


>Don’t do it to anyone unless you’d also slash their tires.

I really do not understand the reasoning behind this statement.

Sabotage of the belief system and slashing tires are very different. Fundamentally different I would say.

Slashing tires leads to an outcome that becomes very quickly obvious to the victim and is easily repairable.

Sabotage of the belief system goes very likely unnoticed to a person and can last for hundreds generations and is very difficult to repair.


All the more convenient, then, that sabotage-of-beliefs is not per se a crime.


I would word it more carefully.

Sabotage of beliefs is not understood to be a crime.

If people understood how much damage it could cause then they perhaps would reconsider it.


> sabotaging someone's beliefs is illegal iff the "someone" is a court of law or government official, or if the belief-being-sabotaged is about a living person such that a falsehood constitutes slander.

Or if you're doing it for personal gain, in which case it may be fraud.


The point here is intent. Don't promote less than maximally accurate beliefs unless you hate someone so much you'd be willing to go and slash their tires.

Also, in terms of real-world consequences, sabotaging someone's thinking can be very, very much worse than just breaking their car.


> The point here is intent.

I see.

> Don't promote less than maximally accurate beliefs unless you hate someone so much you'd be willing to go and slash their tires.

Yet is it not conceivable to hate someone thoroughly, but not enough to be willing to sacrifice one's entire career/reputation/criminal-record by committing any kind of actual crime?


Of course it is. The quote is just pointing out that promoting inaccurate belief is doing actual harm to others.


Ok but anyway, either they were ignorant or they simply lied in the press release. Choose freely what shows the project members in a better light! (Neither? ;)

My initial quotation was this from the press release:

The architects said the aluminium design is derived from John Conway's Game of Life 'cellular automaton',

http://www.cambridge-news.co.uk/news/cambridge-news/could-ca...

You can't protect this with some kind of "we all come from gogol's overcoat", mentality. If it is true then they should have put a Gogol image there! ;)


The architects probably don't have much control over the marketing. They're each doing their jobs.


If they have a sign somewhere in the train station explaining the panels and how they "celebrate GoL" with an explanation of that algorithm then I would have an issue. But I agree that a static image of, ie a 77P6H1V1 wouldn't be a good representation of how it looks when flying.

Static: http://www.conwaylife.com/w/images/8/89/77p6h1v1.png

Animated: http://www.conwaylife.com/wiki/77P6H1V1


>> if you picked ideological purity over pragmatism you wouldn't be a great engineer.

OOoh, disagree. What yields purity is the clash of a pure vision with the constraints of reality. You can't be really "pragmatic" until you've tried really hard to "do the right thing" and failed and looked for alternatives. If you don't even try, you're not being "pragmatic"; just lazy and boring.


The assumption of stupidity, is itself stupid.

What if they decided to go with Rule30 instead of GoL, precisely because they knew there'd be geeks out here that would be arguing about these things, infinitely, while a majority of people will just think its a great example of the kind of mathematical complexity that exists in the universe, either way you look at it?


So is it a hack? Simply: a Shakespeare festival with T.S. Eliot can get much more press coverage?

People like "alternative facts" - both on the believer and the debater side, so give em' what they want for fun and profit? :) That is a fine point, but I simply do not like the value system behind it: to be ignorant or pretend to be ignorant because that's what people like


<meta> I long for the time where HN will not allow the same contributor to respond infinitely to the same thread. If you couldn't get your point across after 4 messages, maybe it's a sign that you shouldn't try just one more time.

You were already given several times the same reasonable explanation. It looks like GoL, and if the architects had said "we used 'rule 30'", absolutely no one would have had a clue what they are talking about. By saying they were inspired by GoL, at least a few people will think 'I vaguely heard of that, it's cool'. It's called pedagogy. Sometimes, being 100% accurate is not helpful.


There were multiple different assumptions why Rule 30 was used, if I think neither is a good reason to use it to tribute Conway, why couldn't I answer them one by one?

It is just my opinion - it is not hard science but art, so maybe no one can be right here: you can just choose not to read my comments if you anticipate in advance that you will disagree ;)

edit: By the way they not said "inspired" by GoL but that they derived the pattern from it. I admit I'm not a native english speaker but I feel some difference... For you if it is the same, or it is fine "pedagogically" then good for you.


> They're professionals like you. Give them some credit.

Ha ha. There's professional courtesy, but at the same time there are annoying truths (like rampant ignorance perhaps only barely above the general population, depending on the profession) we don't like to discuss in an unspoken agreement.

Honestly it just seems like a poorly communicated marketing blurb more than anything else. They wanted to say it's based on cellular automata because they're cool, and they can link the location to a guy somewhat famous even in the general population for something to do with automata (under the phrase GoL). An analogous situation might be some architecture using a Sierpinski pattern and having a blurb on how they derived it from fractals, and could relate the location to Mandelbrot.


>Maybe they were going for the randomness that rule 30 provides (you can build a PRNG from it) but Game of Life doesn't?

You can build a PRNG in Game of Life, since you can build a Turing Machine.

http://rendell-attic.org/gol/tm.htm


Isn't rule 30 also Turing complete? Therefore GoL and rule 30 can both emulate the other, modulo possible exponential blowups in time/space requirements.


No, rule 30 isn't known to be Turing complete. You're probably thinking of rule 110.


Actually, according to the extended Church-Turing thesis, all Turing complete systems can emulate each other with at most polynomial overhead, so no exponential blow-ups.

The only possible exception we know of is quantum computers.


Life. Don't talk to me about life.

https://www.youtube.com/watch?v=CAA67a2-Klk


I'd guess that GoL and Cellular Automaton Theory preceded and inspired rule 30 etc. So, maybe the architects implied metarecursion, that GoL metaphorically generated rule 30.

GoL is Turing complete. I guess that means there is a starting condition that converges to a rule30 cellular automaton.

edit: video of GoL emulated inside a turing machine in GoL https://www.youtube.com/watch?v=xP5-iIeKXE8 (link replaced)


Not sure what post-modernism has to do with such a twisted artistic message, haha.



That's structuralism not postmodernism. Roland Barthes is a structuralist.


Mistakes have been known to happen, like carving the wrong value for pi into a wall:

https://en.wikipedia.org/wiki/Washington_Park_MAX_Station#El...


Maybe they didn't want gun patterns for safety reasons :) But seriously, static patterns work better for medium that is architecture. I just find it so ironic that Wolfram thought this is homage to HIS work. Does he ever mention Conway in any of his texts?


He didn't say once in the entire article that he thought it was a homage to his work. He simply said it used his favorite rule. Everything he writes is about the beauty of this part of the 'computational universe', about giving the architects credit for choosing a pattern which blocks on average 50% of the light, about how they could potentially have extended the work to use more of the pattern. It's a very interesting article with very little of SW's infamous blow-hardiness in it.

In other words, no "Wow Cambridge honored me and my amazing automata!", lots of "These patterns I've loved for years are on a building and that is really exciting."


>Does he ever mention Conway in any of his texts?

For "A New Kind of Science", here is the index entry:

    Conway, John H. (England/USA, 1937- )
      and arithmetic recurrences, 1115
      and Game of Life, 877, 880, 949
      and iterated run-length encoding, 905
      and non-periodic tilings, 943
      in Preface, xiii
      and recursive sequences, 907
      and universality of Life, 1117
https://www.wolframscience.com/nks/index/names/a-e.php?Searc...


I mean it's literally a pattern from Wolfram's cellular automaton, even Conway himself wouldn't think it represents Game of Life.


Not in this one, for sure ...

That is one damn insecure guy.


It's not really wrong, because GoL is Turing Complete.


Who's to say that it isn't a pattern from Game of Life? You can set up the initial configuration however you like.


There's a thing called a "Garden of Eden" configuration that has no predecessors, which is impossible to get to from any other possible state.

For a rule like Life, there are many possible configurations that must have been created by God or somebody with a bitmap editor (or somebody who thinks he's God and uses Mathematica as a bitmap editor, like Stephen Wolfram ;), because it would have been impossible for the Life rule to evolve into those states. For example, with the "Life" rule, no possible configuration of cells could ever evolve into all cells with the value "1".

https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_autom...

For a rule that simply sets the cell value to zero, all configurations other than pure zeros are garden of eden states, and they all lead directly into a one step attractor of all zeros which always evolves back into itself, all zeros again and again (the shortest possible attractor loop that leads directly to itself).

There is a way of graphically visualizing that global rule state space, which gives insight into the behavior of the rule and the texture and complexity of its state space!

Andrew Wuensche and Mike Lesser published a gorgeous coffee table book entitled "The Global Dynamics of Cellular Automata" that plots out the possible "Garden of Eden" states and the "Basins of Attraction" they lead into of many different one-dimensional cellular automata like rule 30.

http://uncomp.uwe.ac.uk/wuensche/gdca.html

The beautiful color plates begin on page 79 in the free pdf file:

http://uncomp.uwe.ac.uk/wuensche/downloads/papers/global_dyn...

I've uploaded the money shots to imgur:

http://imgur.com/gallery/s3dhz

Those are not pictures of 1-d cellular automata rule cell states on a grid themselves, but they are actually graphs of the abstract global state space, showing merging and looping trajectories (but not branching since the rules are deterministic -- time flows from the garden of eden leaf tips around the perimeter into (then around) the basin of attractor loops in the center, merging like springs (GOE) into tributaries into rivers into the ocean (BOA)).

The rest of the book is an atlas of all possible 1-d rules of a particular rule numbering system (like rule 30, etc), and the last image is the legend.

He developed a technique of computing and plotting the topology network of all possible states a CA can get into -- tips are "garden of eden" states that no other states can lead to, and loops are "basins of attraction".

Here is the illustration of "rule 30" from page 144 (the legend explaining it is the last photo in the above album). [I am presuming it's using the same rule numbering system as Wolfram but I'm not sure -- EDIT: I visually checked the "space time pattern from a singleton seed" thumbnail against the illustration in the article, and yes it matches rule 30!]

http://imgur.com/a/lKAbP

"The Global Dynamics of Cellular Automata introduces a powerful new perspective for the study of discrete dynamical systems. After first looking at the unique trajectory of a system's future, an algoritm is presented that directly computes the multiple merging trajectories of the systems past. A given cellular automaton will "crystallize" state space into a set of basins of attraction that typically have a topology of trees rooted on attractor cycles. Portraits of these objects are made accessible through computer generated graphics. The "Atlas" presents a complete class of such objects, and is inteded , with the accompanying software, as an aid to navigation into the vast reaches of rule behaviour space. The book will appeal to students and researchers interested in cellular automata, complex systems, computational theory, artificial life, neural networks, and aspects of genetics."

https://en.wikipedia.org/wiki/Attractor

"Basins of attraction in cellular automata", by Andrew Wuensche:

http://onlinelibrary.wiley.com/doi/10.1002/1099-0526(200007/...

"To achieve the global perspective. I devised a general method for running CA backwards in time to compute a state's predecessors with a direct reverse algorithm. So the predecessors of predecessors, and so on, can be computed, revealing the complete subtree including the "leaves," states without predecessors, the so-called “garden-of-Eden" states.

Trajectories must lead to attractors in a finite CA, so a basin of attraction is composed of merging trajectories, trees, rooted on the states making up the attractor cycle with a period of one or more. State-space is organized by the "physics" underlying the dynamic behavior into a number of these basins of attraction, making up the basin of attraction field."


Fascinating, thank you very much. To me a completely novel way to think about CA. Going to have a play with this.


Never heard of this book, thanks for sharing.



Yeah that's the problem with unconstrained things: http://dilbert.com/strip/2001-10-25

(Ok-ok, I know it is just a fun comment, but just to be serious anyway for the sake of truth:

you can think of how likely that this is a GoL pattern: take the set of all imaginable GoL patterns, at all timestep, and check how frequent is this subpattern then, compared to some combination of some common/well-know patterns, like these: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Exampl... )


I guess it is because GoL is 2D, so you cannot visualize the dynamics in 2D, you could just show a single generation. Instead they went for an interesting looking simple 1D cellular automaton.


I think it is funny, Conway doesn't really enjoy being solely associated with GOL and the fame it brings[0].. In stark contrast with Wolfram's ego. Perhaps this arrangement actually works out best for both of them.

[0]https://www.youtube.com/watch?v=E8kUJL04ELA


I choose to think of it as the Game of Life simulating rule 30, but zoomed way out.

Or maybe this is a joke at Wolfram's expense, attributing one of his own to Conway.


This is the quintessential hacker news post, IMO.

A topic that on the surface seems run of the mill (a train station)

Technical in its essence

Authored by someone notable (in this case really notable, which is not a requirement)

My comment on the other hand, not in the spirit of the discussions on HN but I like to celebrate good posts when I see them.


If anyones interested I wrote some JS to view states 0 to 255 in canvas. http://www.kaundur.com/jekyll/update/2016/10/31/cellular-aut...


Anyone know the origin of the 22,000 BC pattern? I had no idea anyone was making such impressively detailed masonry that far back.

The Sumerian columns with geometric mosaics are pretty cool too.


Brilliant spot! I hadn't read that in the local papers - there was simply criticism of the 'boxy' design. I live right by that station, and used it for the first time this weekend (only a few days after it opened) and my wife and I commented on the attractive appearance of it.

Despite some controversies (are there enough ticket machines, enough toilets, enough train services, and so on...) Cambridge North is going to become a popular station.


So... who're the architect(s) for the station? How did they go about laying the tiling on that facade, programming the CNC to cut the pattern in the aluminium, etc.? Sounds like there are probably some interesting people behind it all.


In A New Kind of Science, Wolfram made the bold conjecture that the whole universe might be a cellular automaton. So there doesn't necessarily have to be a designer: it could just be part of the fabric of the universe itself, just as he breathtakingly predicted! I mean, he wasn't really thinking of train stations when he wrote that, it's not exactly the validation he would have liked... but I think at this point he'll take what he can get :)

-

EDIT: downvotes but I thought this was funny :)


Did Wolfram give any clue about how e.g. relativity may emerge from a cellular automaton?


I think he might have. It's been a long time since I read his book, but see here: https://www.wolframscience.com/nks/chap-9--fundamental-physi....

I also remember reading elsewhere that e.g. speed of light (as a finite information speed limit) limit emerges straight out of casual networks generalized to be continuous instead of discrete.


Which relativity? :) No idea about Wolfram but special relativity doesn't need very many assumptions; you can do it if all you assume are causal sets and a quantification scheme: https://arxiv.org/abs/1005.4172 And since Conway's GoL is Turing-complete, you could maybe construct something using the Strong Church–Turing thesis.


You can make some pretty fun tilings out of Penrose tiles as well. My wife and I made a ceramic-tile headboard out of the Penrose P2 tiling (an aperiodic tiling) that looks quite lovely - the tiles, being handmade, avoid sterility. Like the patterns in the OP, they have recurring themes, but don't fully repeat.


Penrose tilings would look much better, yes. They are proven to be aperiodic. Penrose' alma mater was St.John's in Cambridge but then he switched to be professor at Oxford, in the south. So they cannot really put Penrose tilings on a Cambridge station. There's huge rivalry between those two cities.

But how could they fuck up Conway with Wolfram tilings? Wolfram went to St.John's in Oxford and then moved to California. No Cambridge there. Conway's alma mater was in Cambridge and then he became professor in Princeton, USA. Penrose has the same affiliations as Conway, the only problem is that Penrose stayed in the UK and went to Oxford.


There is a 'Penrose Paving' outside the new Mathematical Institue in Oxford (the Andrew Wiles building), which opened in 2013.

There's a video of Roger Penrose talking about it [1], and a time-lapse of it being laid [2].

[1]: https://www.maths.ox.ac.uk/node/865

[3]: https://www.maths.ox.ac.uk/about-us/our-building



I made a set of ten cellular automata posters for my office wall y'all might like! Let me know if you'd like me to send out some high res versions.

https://imgur.com/a/cz7V2


Those are beautiful.


Thanks! Made them using Processing.org then printed them in high resolution for the wall. Turned out really nicely!


I'm pretty new to CA, so I found this really useful in giving some necessary background to the algorithm and what a "rule" is: http://natureofcode.com/book/chapter-7-cellular-automata/


Fantastic post. Opened me up to some mathematics I didn't know about. But please Wolf, these pictures are tiny.


One of the most coolest posts i've seen lately.

I did not know such patterns were also present in antique art. I guess one learns a cool thing every day !


Well look into Ancient Greeks they were already relating beauty and math. Hard to say where it came out first but they started noticing patterns in music and from there to associating art to mathematical proportion was a short step


the fashion online shop asos.com also uses a pattern that looks like a cellular automaton for it's packaging:

https://twitter.com/laurenadams7/status/632178492503912448


Maybe, the should have used one of the many repeating Rule 30 patterns: http://www.iwriteiam.nl/Rule30.html


Uncanny and amazing


Very nice!


We get it - cellular automata. This would have been an interesting article if he had tracked the artist/architects, interviewed them and asked them how they ended up with these patterns, what tools they used etc.

Instead it's the same endless blabber about the damn automata we have heard for the last 20 years.


Why do multiples of '512' using the Wolfram alpha automata panels show dark gray canvases?

(For example, 512,1024,2048, etc...)

https://www.wolframcloud.com/objects/sw-blog/capanels


Well they do make nice PRNGs.


I've long been a fan of Wolfram's ideas. But I wish he could write a single thing without most of it being about: how great he is, and how he has supposedly made the most progress in history with a cognitive step from already explored cellular automata. It's not even that I'm that bothered by the arrogance, it's just repetitive and boring.


When I read the article, I didn't know it was written be Stephen Wolfram. It sounded like any other math/tech blogger. He'd played with these things when he was younger, similar to what many programmers have done. And he was excited to find something familiar on a public building. It sounded completely non-arrogant to me. I used to play with fractals and would be just as excited to see my familiar toy on a public building, even though I didn't discover them.

He didn't claim to have invented it, or that the building was designed in his honor. I think you have to be expecting arrogance to see it in this article.


No, he does. He even calls his cataloging of different runs of CA permutations his "discovery" as in "when I discovered".


I took that as talking about the moment he discovered rule 30 (just like I discovered it myself at one point in my life). It doesn't sound like he's claiming the be "the discoverer" of it.

On the other hand, he might very well be the actual discoverer, anyway.


He was the first to describe this form of CA and systematically investigate the results of the different rule sets.


You are afflicted with Wolfram Derangement Syndrome: https://news.ycombinator.com/item?id=10978871

There is a way out. I believe in you!


The problem with dang's wish stated in the linked thread is that the goal is most likely unattainable.

While the community as a whole has a collective memory, that does not mean that every participant has the sum of all that experience and knowledge, because individuals constantly join and leave the community.

This means that for some parts of the community, every new post (in this case by Wolfram) is one of "The first few times this came up" when it was "worth noting (and I confess to laughing at the same parodies that everyone else did)".

Because of the nature of Hacker News (the focus on individual stories (links)) the only way for new members of the community to be "nudged in the right direction", as it were, is to come upon one of these comment sections and either see the problem for themselves or see it called out (as here).


The fun thing about that discussion is note in the first reply:

"[When there is a single Official Wolfram Ego Bitching subhthread in every thread discussing Wolfram], then everyone can enjoy complaining about Wolfram's ego there, without it taking over the rest of the discussion. (This would work better if HN offered a way to "collapse" subthreads.)"

And now we actually have collapsable subthreads!

* proceeds to collapse grandparent


The deranged Wolfram story I find most delightful is about the pains he took micromanaging the illustrations in his book, and how hard he is to work for. He required a photo of a leopard, to illustrate how its spots were similar to a reaction diffusion system. But he rejected the first leopard photo and demanded it be replaced by another, because he didn't like its facial expression.


Doesn't sound weird at all. If I would be writing a book, I would like to direct what kind of photos it includes.


Oh yes, I think it's charming how aesthetically picky he was about which cat pictures to use in his book. It's not enough for the science and mathematics behind the gigantic book to be ground breaking, revolutionary, earth shattering and astounding -- but also the leopard's smirk can't give readers the wrong impression.


Ok, point taken, it's a dead horse. Is there an argument that ignoring social pathology and carrying on is dangerous in the long run though?


The alternative is to register the pathology as known, considered, addressed, and ... not of particular interest in the current context.

dang's post attempts to do this. HN has poor tools for surfacing such actions and intentions (it has poor tools in a large number of ways, but the very tool paucity also creates, at times, some useful positive dynamics).

Sometimes you want low friction, sometimes you want high friction.

A wheel, particularly in the flanged steel-on-rail or rubber tyre-on-road varieties, is a device for offering exceptionally low friction and resistance in one dimension, and very high resistance in another. Among the results of such a dynamic is the property, literally, of keeping a vehicle on track.

I think HN's quirks of high- and low-affordance capabilties operate somewhat in this nature.


The argument is that going on about it in every single Wolfram thread is just as quickly "repetitive and boring" and worse, makes it impossible to actually talk about whatever it is that Wolfram is writing about. It's hardly ignoring if everyone already knows about it and the chances of anyone saying anything new and interesting on the topic is just about nil.


There's an argument, sure, but you're basically arguing against the entire concepts of politics and perspective.


I dunno, if people weren't so bored of fact checkers pointing out lies, maybe we wouldn't be in this mess.


I think we're all forgetting that the prime reason Wolfram has a blog IS to expound on his ideas, and showcase the versatile uses of his Mathematica software, in the same way Google, Microsoft or ordinary developers have their own blogs.

But for some reason, people expect his posts to be general commentaries about science, math or computing, like a Scientific American Blog post - perhaps it's due to his reputation as a 'genius', which makes people forget he is also a CEO.


Wolfram reminds me of Richard Feynman, in that sense.

The first time I tried to read "Surely You're Joking" as a kid I had to put it down -- the incessant "ME! ME! ME!" dripping from every page was a little too much.

I've since mellowed down and can read Feynman or Wolfram without any issues. I even enjoy that style now :-)


What were you expecting from a biography?


Some humility mixed in with his bragging? Seems like a fair ask.


You're not the only one, Murray Gell-Mann regarded Feynman as self-aggrandising.

I still liked "Surely You're Joking" though. A lot, even though I've come to regard Feynman as somewhat flawed.


The first time I tried to read a Feynman Diagram as a kid I had to put it down -- the incessant "ME! ME! ME!" dripping from every subatomic particle was a little too much.


Okay now you're just being contrary. Everyone knows that subatomic particles are all, like, "YOU! YOU! YOU!" ..


4/3 I's per paragraph


It's pretty ceaseless, too, down to the names he gives everything (his name).


At least this was relatively to the point, whenever I've read something from him in the past it's more like a 72 page treatise on cellular automata followed by the two line grilled cheese sandwich review the title promised.


I read the article and didn't feel the same way, what stood out to you specifically?


Wolfram's writing style is a known thing; I suspect that GP is currently hypersensitive to it, and sees lots of false positives.

"I know Woflram has ego issues in his writings, therefore this perfectly neutral sentence must be in fact Wolfram congratulating himself!".


Here's a start: "Here’s a website (made in a couple of minutes with a tiny piece of Wolfram Language code)". He's bragging about his coding prowess, selling his product and basking in the pleasure of writing his own name, all at once. :)


This intrigues me because I never see the self-aggrandizement.

> bragging

I got that he was saying how easy it was for anyone, not just him. Not bragging.

> selling his product

To be fair it wouldn't show a lot of confidence if he never used it

> writing his own name

It's the name of the language. What do you want him to say, "a certain language who's name I will not disclose"? :)


The issue is why bring up the language at all? Why even mention that it was written "in a few lines of Wolfram", rather than just pointing people to the source? Because that's how advertisers speak. They don't say "this coffee is delicious" they say "This single-source Starbucks coffee is delicious."

You can speak the truth and be informative while still maintaining your dignity and respecting other people's right to objectivity. He's not doing that. He's asking you to sacrifice your objectivity because it serves him. The self-aggrandizing tone he takes is an affront to the objective simplicity of truth -- that even if he wasn't here to do the things he does, they would still be doable. He writes as though this is not true.

He doesn't just say "Rule 30 is one of those rules that has an 'organic' feel to it." He says something like "This Rule 30 that I discovered, is what I call a 'class 4' rule -- one that has an organic feel." It's like he has a compulsive inability to separate plain facts from his own brand. He has to constantly remind you that he is the god who made these things possible.


If I had a language that could do a cool microsite in just few lines of my language code I'd be pretty proud of it too.


I wouldn't say so -- for a professional programmer, rule 30 is pretty fucking easy to implement in a few minutes, especially in Wolfram Language. It's trivial, not rocket science, nor much to brag about. But if you take him as bragging about implementing Mathematica / Alpha / Wolfram Language itself, well at least that's something worth bragging about.


I agree, it does get old fairly quickly. I also don't think cellular automata has made the giant "new kind of science" impact that he proposed that it would.


On closer inspection, it's not arrogance. It the sort of literary solipsism that companies use in their PR communications.


That the author would focus purely on his PoV fits with what I read about the author's character. I was reading and wondering why he wouldn't inquire and link to an official statement.


We detached this subthread from https://news.ycombinator.com/item?id=14467718 and marked it off-topic.



> That the author would focus purely on his PoV fits with

"this being a casual blog.", I believe is how that sentence is supposed to end.


a 1000 word article doesn't quite strike me as casual.


The length seems pretty typical to me. Most of the text actually goes to explaining pictures.


A somewhat relevant "theory of everything" in a TED video from 8 years ago:

https://www.youtube.com/watch?v=aoy4t_zAJJ4


This guy really thinks he invented cellular automata.


Just a shame there are no direct trains to or from London to Cambridge North, eh?!


There are. Even some reasonably fast ones, the fast train I got from London to Cambridge was stopping there next stop just the other day.


How many human beings on the planet could have seen that pattern, realized it was familiar, and then figured out what it was? It's like an inside practical joke, or, the ultimate Easter Egg.


Lots of people. That's why Wolfram kept getting requests to identify it. That's why the building was designed with that pattern. It's not like there's anything particularly obscure here.


Hmm. This is a train station, yes? What % of people transiting the station see that pattern and think, 'Oh, that's a cellular automata.'. Clearly more than zero, and perhaps it's not considered obscure by HN readers, but likely a very, very small % of passengers will recognize what it is. Wolfram himself seemed to be surprised.


I guess I just got the sense from your post that it would take a 1-in-6-billion person to recognize the pattern rather than something more realistic like 1-in-ten-thousand.




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