9 ms·

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

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-view/view/cambridge-science-park-station-to-incorporate-game-of-life.html http://www.railwaygazette.com/news/infrastructure/single-vie...

szemet 9y ago
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...
- damnyou 9y ago
  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?
  - szemet 9y ago
    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. ;)
    - damnyou 9y ago
      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-reason-cellular-automaton-on-the-new-cambridge-north-station/#comment-780944 http://aperiodical.com/2017/05/right-answer-for-the-wrong-re... They're professionals like you. Give them some credit.
      - szemet 9y ago
        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!"
        damnyou 9y ago
        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.
        mnsc 9y ago
        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 http://www.conwaylife.com/w/images/8/89/77p6h1v1.png Animated: http://www.conwaylife.com/wiki/77P6H1V1 http://www.conwaylife.com/wiki/77P6H1V1
        szemet 9y ago
        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-cambridge-north-station-owe-13111740 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! ;)
    - samirillian 9y ago
      Not sure what post-modernism has to do with such a twisted artistic message, haha.
      - szemet 9y ago
        https://www.quora.com/Why-do-post-modern-artists-question-authorship-in-contemporary-art https://www.quora.com/Why-do-post-modern-artists-question-au...
        samirillian 9y ago
        That's structuralism not postmodernism. Roland Barthes is a structuralist.
    - posterboy 9y ago
      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 https://www.youtube.com/watch?v=xP5-iIeKXE8 (link replaced)
  - veli_joza 9y ago
    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?
    - Grue3 9y ago
      I mean it's literally a pattern from Wolfram's cellular automaton, even Conway himself wouldn't think it represents Game of Life.
    - B1FF_PSUVM 9y ago
      Not in this one, for sure ... That is one damn insecure guy.
    - scrumper 9y ago
      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."
    - xrange 9y ago
      >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?SearchIndex=Conway%2C%20John%20H.#searchword1/ https://www.wolframscience.com/nks/index/names/a-e.php?Searc...
  - xrange 9y ago
    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#Elevators https://en.wikipedia.org/wiki/Washington_Park_MAX_Station#El...
- anonymfus 9y ago
  May be they consulted with Stephen Wolfram.
- chillingeffect 9y ago
  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 :)
  - patcon 9y ago
    Very nicely said! I really enjoyed your comment :)
- posterboy 9y ago
  It's not really wrong, because GoL is Turing Complete.
- brenschluss 9y ago
  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.
  - chris_va 9y ago
    waterjet, probably, and I don't think it would be too pricey since you can stack many sheets.
    - brenschluss 9y ago
      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.
qf303rjr3 9y ago
Who's to say that it isn't a pattern from Game of Life? You can set up the initial configuration however you like.
- szemet 9y ago
  Yeah that's the problem with unconstrained things: http://dilbert.com/strip/2001-10-25 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#Examples_of_patterns https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Exampl... )
- DonHopkins 9y ago
  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_automaton) 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 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_dynamics_of_CA.pdf http://uncomp.uwe.ac.uk/wuensche/downloads/papers/global_dyn... I've uploaded the money shots to imgur: http://imgur.com/gallery/s3dhz 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 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 https://en.wikipedia.org/wiki/Attractor "Basins of attraction in cellular automata", by Andrew Wuensche: http://onlinelibrary.wiley.com/doi/10.1002/1099-0526(200007/08)5:6%3C19::AID-CPLX5%3E3.0.CO;2-J/full 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."
Isamu 9y ago
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.
splawn 9y ago
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 https://www.youtube.com/watch?v=E8kUJL04ELA
doetoe 9y ago
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.

szemet 9y ago

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...

damnyou 9y ago
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?
- szemet 9y ago
  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. ;)
  - damnyou 9y ago
    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-reason-cellular-automaton-on-the-new-cambridge-north-station/#comment-780944 http://aperiodical.com/2017/05/right-answer-for-the-wrong-re... They're professionals like you. Give them some credit.
    - szemet 9y ago
      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!"
      - damnyou 9y ago
        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.
        mnsc 9y ago
        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 http://www.conwaylife.com/w/images/8/89/77p6h1v1.png Animated: http://www.conwaylife.com/wiki/77P6H1V1 http://www.conwaylife.com/wiki/77P6H1V1
        szemet 9y ago
        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-cambridge-north-station-owe-13111740 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! ;)
  - samirillian 9y ago
    Not sure what post-modernism has to do with such a twisted artistic message, haha.
    - szemet 9y ago
      https://www.quora.com/Why-do-post-modern-artists-question-authorship-in-contemporary-art https://www.quora.com/Why-do-post-modern-artists-question-au...
      - samirillian 9y ago
        That's structuralism not postmodernism. Roland Barthes is a structuralist.
  - posterboy 9y ago
    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 https://www.youtube.com/watch?v=xP5-iIeKXE8 (link replaced)
- veli_joza 9y ago
  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?
  - Grue3 9y ago
    I mean it's literally a pattern from Wolfram's cellular automaton, even Conway himself wouldn't think it represents Game of Life.
  - B1FF_PSUVM 9y ago
    Not in this one, for sure ... That is one damn insecure guy.
  - scrumper 9y ago
    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."
  - xrange 9y ago
    >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?SearchIndex=Conway%2C%20John%20H.#searchword1/ https://www.wolframscience.com/nks/index/names/a-e.php?Searc...
- xrange 9y ago
  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#Elevators https://en.wikipedia.org/wiki/Washington_Park_MAX_Station#El...
anonymfus 9y ago
May be they consulted with Stephen Wolfram.
chillingeffect 9y ago
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 :)
- patcon 9y ago
  Very nicely said! I really enjoyed your comment :)
posterboy 9y ago
It's not really wrong, because GoL is Turing Complete.
brenschluss 9y ago
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.
- chris_va 9y ago
  waterjet, probably, and I don't think it would be too pricey since you can stack many sheets.
  - brenschluss 9y ago
    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.

qf303rjr3 9y ago

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

szemet 9y ago
Yeah that's the problem with unconstrained things: http://dilbert.com/strip/2001-10-25 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#Examples_of_patterns https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Exampl... )
DonHopkins 9y ago
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_automaton) 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 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_dynamics_of_CA.pdf http://uncomp.uwe.ac.uk/wuensche/downloads/papers/global_dyn... I've uploaded the money shots to imgur: http://imgur.com/gallery/s3dhz 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 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 https://en.wikipedia.org/wiki/Attractor "Basins of attraction in cellular automata", by Andrew Wuensche: http://onlinelibrary.wiley.com/doi/10.1002/1099-0526(200007/08)5:6%3C19::AID-CPLX5%3E3.0.CO;2-J/full 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."

Isamu 9y ago

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.

splawn 9y ago

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

doetoe 9y ago

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.