![]() ![]() And so a universal constructor can be regarded as any system (glider-based or otherwise) allowing a recipe for every possible glider construction. While gliders colliding aren’t as powerful as just scribbling a pattern of your choosing ( notable examples), they’re pretty darn close. There is now a footnote on the corresponding wiki page saying that it can be constructed in fewer using RCT. This easy-to-watch synthesis takes 33 gliders. For a canonical baseline, we can use arbitrary collections of gliders converging from infinity, like in the pattern below synthesizing a “weekender” spaceship. Systems are equivalent if they can build all of the same things, regardless of efficiency. In shifting back to Conway’s Game of Life, replace computation by construction. Any system with equivalent computational ability, is deemed “Turing Complete”. ![]() Despite being neither the most nor least efficient example of a computer, the Turing Machine is the canonical baseline for computational ability. And similarly, one often hears that much weaker systems, like Rule 110, are just as powerful as a Turing Machine. One often hears that a Turing Machine is just as powerful as a modern computer, in that it can run all of the same algorithms (but maybe taking more time). I’ll try to treat the topic a little better this time around, by analogy to Turing Machines. Universal constructors came up in my Waterbear post as well. In his words:Īs long as we can synthesise a universal constructor in 385, the entire blueprint could be encoded in the *distance* between the final glider and the constructor (by Godel coding or otherwise). But rather, plausible that a super-complex pattern can be synthesized in a relatively small number of gliders. Not plausible in origin, as the story was just the brainchild of an internet troll. Gustavo said that through his eavesdropping, he learned that a previously unknown spaceship, larger than the Caterpillar, had a synthesis in 386 gliders.Īdam Goucher, a mathematician of some notoriety and author of the cp4space blog, treated this as plausible. User “gameoflifeboy” described it as “the weirdest thread on the forum so far in 2015”. Some people trying to humor Gustavo, asking for proof, others trying to make the inconsistencies in his story more obvious.Įverything about this story was imaginative nonsense, with no substance. The community interaction with this thread was honestly hilarious. In a new thread, Gustavo rambled about a secret leaked Morse code signal from MIT he was decoding, which seemed to be discussing “Game of Life – Spaceship Synthesis Research”. It began with Gustavo, a Conway’s Game of Life enthusiast from Brazil who had a tendency to go far off topic in the forums. The prompt to get people thinking about this came in 2015, in a truly bizarre fashion. The fact that we need to use a lot of distance, guides us to our first principle. This is possible, but only by taking advantage of a correspondingly unbounded amount of distance between at least one pair of gliders in the recipe. Since we have infinitely many patterns to create, we must list infinitely many 15 glider arrangements. With 15 gliders (or any fixed number), the only difference between one initial set and another is where they start. Every one of these patterns needs a different initial set of gliders. How is this even possible?įrom an information theory perspective, an arbitrary selected pattern can have unbounded amounts of complexity. This post will talk about how it works, how we got there, and why it’s so cool. No extra leftover debris, no stray scaffolding, just a pure synthesis of whatever you chose. After enough time goes by, those gliders need to build that pattern. Begin with a small number of gliders (now 15) in an otherwise empty Game of Life universe. Select any pattern that can be built in Life – for example, the Waterbear. An idea years in the making, the “Reverse Caber Tosser” design finally had all of the pieces it needed to achieve its stated goal. The Conway’s Game of Life community celebrated a landmark achievement on November 9th, 2022. Building arbitrary Life patterns in 15 gliders ![]()
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