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This has me thinking about Wolfram's four classes of behavior for simple programs [1]. He hypothesizes that the irreducible complexity of class 3 rules means th

This has me thinking about Wolfram's four classes of behavior for simple programs [1]. He hypothesizes that the irreducible complexity of class 3 rules means that they are Turing complete, and in a sense maximally complex, which has been proved for at least some class 4 rules. The class 4 behavior is more "interesting" though, if only in the way those patterns yield to analysis, but to determine what types of programs express such behavior may be a priori impossible. In the end, finding "useful" patterns may come down to a brute force "mining of computational space". [1] https://www.wolframscience.com/nks/p231--four-classes-of-behavior/ https://www.wolframscience.com/nks/p231--four-classes-of-beh...

eggy 3y ago
Re-reading parts of Andrew Ilachinski's, 'Cellular Automata: A Discrete Universe' and Wolfram's 'A New Kind of Science', and this classification intrigued me. I was looking for more than the statement on the classes of rules, and I didn't find the formal explanation. Very cool stuff cellular automata! Ilachinski's book is amazing in its scope and still very relevant from it's over twenty-year publication date. I am currently reading his book, 'Artificial War: Multiagent-Based Simulation of Combat'.
- arketyp 3y ago
  > I was looking for more than the statement on the classes of rules, and I didn't find the formal explanation Yes. Wolfram gets the point across, but the lack of formality makes the taxonomy appear somewhat arbitrary which leaves one hanging. Thanks for the tip about Ilachinski's book. I notice it was published around the same time as NKS which makes me curious about the overlap in content; it certainly seems to have a more formal approach.
  - eggy 3y ago
    Ilachinski's book cites Wolfram's 1980s article as a pivotal moment on top of the previous history with CA, but he goes into everything - complexity, CA, neural networks, genetic algorithms, etc. It is an amazing book, and I thoroughly enjoy his exposition and breadth of knowledge. I started with neural networks and evolutionary computing back in the late 80s. His book is a great survey book with great detail too. The Artificial War book is pretty cool. I was into war games (board games back in the 80s), and his multi-agent approach was unique at the time and is fun to play with.
    - arketyp 3y ago
      Thanks. It's nice to hear the 80's article was acknowledged. Game theory dynamics are fascinating. I have Nowak's Evolutionary Dynamics in my shelf, in which he covers for instance spatial prisoner's dilemma modelled as cellular automata.
      - eggy 3y ago
        I have picked up Nowak's book a few times, but I have not read it. Wolfram's new physic's book is visually appealing, and I am starting it soon. I tried making up my own rules without reference to see just how difficult it is to achieve anything similar to Conway's GoL, and it is eyeopening. I do love the variations on it where the simulations look almost like microscope vids of actual organisms. Artificial Life sims. People are getting creative in these sims, and some produce some beautiful and engaging animations.
        arketyp 3y ago
        The images were always what drew me to NKS, and CA in general obviously. I don't expect to find any answers in them; for me it's a gateway to ontological mysteries. I'm quite content spending time just in wonder.
  - carapace 3y ago
    > the lack of formality makes the taxonomy appear somewhat arbitrary I thought it was empirical? E.g. sample Turing drawings: https://maximecb.github.io/Turing-Drawings/ https://maximecb.github.io/Turing-Drawings/ They clearly seem to me to fall into four kinds: Boring, Oscillating, Chaotic, Life.
    - arketyp 3y ago
      That's true. It's a convention. I thirst for an epistemological investigation, in turn, I suppose.
      - carapace 3y ago
        That's IMO a much more fascinating question. What does it mean that simple systems can exhibit "life"? The first three kinds of simple system are, um, pretty obvious: Boring is static, Oscillators have movement but are static in time so to speak, chaotic systems overwhelm themselves with too much movement, "living" systems seem to balance stasis and chaos. But what does it mean? ;)
        arketyp 3y ago
        Exactly. Glad we share the same view.

eggy 3y ago

Re-reading parts of Andrew Ilachinski's, 'Cellular Automata: A Discrete Universe' and Wolfram's 'A New Kind of Science', and this classification intrigued me. I was looking for more than the statement on the classes of rules, and I didn't find the formal explanation. Very cool stuff cellular automata! Ilachinski's book is amazing in its scope and still very relevant from it's over twenty-year publication date. I am currently reading his book, 'Artificial War: Multiagent-Based Simulation of Combat'.

arketyp 3y ago
> I was looking for more than the statement on the classes of rules, and I didn't find the formal explanation Yes. Wolfram gets the point across, but the lack of formality makes the taxonomy appear somewhat arbitrary which leaves one hanging. Thanks for the tip about Ilachinski's book. I notice it was published around the same time as NKS which makes me curious about the overlap in content; it certainly seems to have a more formal approach.
- eggy 3y ago
  Ilachinski's book cites Wolfram's 1980s article as a pivotal moment on top of the previous history with CA, but he goes into everything - complexity, CA, neural networks, genetic algorithms, etc. It is an amazing book, and I thoroughly enjoy his exposition and breadth of knowledge. I started with neural networks and evolutionary computing back in the late 80s. His book is a great survey book with great detail too. The Artificial War book is pretty cool. I was into war games (board games back in the 80s), and his multi-agent approach was unique at the time and is fun to play with.
  - arketyp 3y ago
    Thanks. It's nice to hear the 80's article was acknowledged. Game theory dynamics are fascinating. I have Nowak's Evolutionary Dynamics in my shelf, in which he covers for instance spatial prisoner's dilemma modelled as cellular automata.
    - eggy 3y ago
      I have picked up Nowak's book a few times, but I have not read it. Wolfram's new physic's book is visually appealing, and I am starting it soon. I tried making up my own rules without reference to see just how difficult it is to achieve anything similar to Conway's GoL, and it is eyeopening. I do love the variations on it where the simulations look almost like microscope vids of actual organisms. Artificial Life sims. People are getting creative in these sims, and some produce some beautiful and engaging animations.
      - arketyp 3y ago
        The images were always what drew me to NKS, and CA in general obviously. I don't expect to find any answers in them; for me it's a gateway to ontological mysteries. I'm quite content spending time just in wonder.
- carapace 3y ago
  > the lack of formality makes the taxonomy appear somewhat arbitrary I thought it was empirical? E.g. sample Turing drawings: https://maximecb.github.io/Turing-Drawings/ https://maximecb.github.io/Turing-Drawings/ They clearly seem to me to fall into four kinds: Boring, Oscillating, Chaotic, Life.
  - arketyp 3y ago
    That's true. It's a convention. I thirst for an epistemological investigation, in turn, I suppose.
    - carapace 3y ago
      That's IMO a much more fascinating question. What does it mean that simple systems can exhibit "life"? The first three kinds of simple system are, um, pretty obvious: Boring is static, Oscillators have movement but are static in time so to speak, chaotic systems overwhelm themselves with too much movement, "living" systems seem to balance stasis and chaos. But what does it mean? ;)
      - arketyp 3y ago
        Exactly. Glad we share the same view.