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Building arbitrary Life patterns in 15 gliders

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Re: Building arbitrary Life patterns in 15 gliders

#91

Post by biggiemac42 »

Grustaf wrote: post #44
biggiemac42 wrote: post #12

Hi there, I'm the author (of the blog post, not of the achievement itself)! So glad this is spreading. Feel free to ask here or on the post for more clarification if stuff is too unclear

Almost everything was unclear to me, but then I'm not familiar with the Game of Life lingo. Perhaps it would make sense to write a version that the educated public can understand, even without any Life background?

I would say "the educated public" is already the target audience for my blog. Game of life topics are notoriously hard to disentangle from their jargon, and I went to some effort here but needed to balance that against the goal to remain accurate.

My hope is that by reading only the amount of background on the blog already in the Waterbear post (referenced immediately in the introduction), you have all you need to grok the post. But that's certainly an optimistic hope, and maybe unfounded.

Re: Building arbitrary Life patterns in 15 gliders

#92

Post by sagebird »

Can automated theorem proving software be coaxed into finding recipes for GOL constructions?

I would find it interesting trying to formalize notions that we easily perceive into computer-understood definitions.

May end up with strange formalizations to make things as orthogonal as possible: IE a beehive is a glider speed zero.

Re: Building arbitrary Life patterns in 15 gliders

#93

Post by OscarCunningham »

isoprophlex wrote: post #88

I had a particularly hard time grokking the way the semilator works to reduce pattern size. It's a pretty difficult term to google too, being so similar to the word 'simulator'. Does anyone well versed in GoL-ogy care to share a short ELI5? Edit: thanks you people for the explanation, makes sense. Nice hack to make it feasible.

So the full-size pattern works by bouncing a signal back-and-forth between the construction site and an oncoming GPSE. Each time it does this it produces either one or two gliders depending on the positioning of the GPSE. It is these gliders that do the construction.

But the 'recipe' contains 1665791 bits, meaning the signal has to bounce back-and-forth 1665791 times. Because the distance to the GPSE halves every time, it would have to start at a distance of 2^1665791, which is impractically large.

So instead we only have it bounce back-and-forth a small number of times (26), and insert the other 1665765 bits 'manually' by adding streams of 1665765 spaceships that collide near the construction site.

Re: Building arbitrary Life patterns in 15 gliders

#94

Post by OscarCunningham »

sagebird wrote: post #92

Can automated theorem proving software be coaxed into finding recipes for GOL constructions? I would find it interesting trying to formalize notions that we easily perceive into computer-understood definitions. May end up with strange formalizations to make things as orthogonal as possible: IE a beehive is a glider speed zero.

I have a program called LLS that uses SAT solvers to find patterns with specified properties. https://conwaylife.com/wiki/Logic_Life_Search But it only works cell-by-cell, so it can't make big patterns like this.

Re: Building arbitrary Life patterns in 15 gliders

#96

Post by isoprophlex »

Strilanc wrote: post #37
OscarCunningham wrote: post #28

Earlier quoted context omitted.

There are still plenty of open problems! Here are some of my favourites: * Is there an oscillator of every possible period? (We have them all except 19 and 41.) * If you start off the entire plane in a random starting state, does its density tend to a limit as time goes to infinity? * Is there a 'phoenix' oscillator, in which every live cell dies every generation, of period greater than 2? * Can every pattern be dest…

I'd be surprised if there was a computable density limit for the random plane, just because the system is Turing complete so the answer could easily end up being like Chaitin's contant where it depends on halting problems. For example, note that an infinite random plane will contain, with probability 1, purely-by-chance prebuilt artificial intelligences with goals like "maximize number of blinkers in the plane". Thou…

If it can be proven that there are no indestructible patterns, your AI can clean up everything around it!

(... and encounter other AIs that act as hegemonising swarms, eg. that populate the plane with copies of themselves)

Re: Building arbitrary Life patterns in 15 gliders

#97

Post by Silverback_VII »

vanderZwan wrote: post #84

Whenever I read one of these deep dives into GoL achievements, and let me preface this by saying I mean this as a compliment, I feel like I'm reading the extended universe lore on a wiki page for a giant fantasy franchise. It's maths but feels so much more narratively rich than most other mathematics somehow, and the community around it has such a unique subculture vibe to it too.

in my opinion Jeffery Ventrella's clusters are a more promising avenue than Conways GoL. The rules are in comparison very interesting as well: No creation out of nothing, only particles that attract or repel each other.

The pattern it generates are pretty amazing as you can see here: https://youtu.be/0Kx4Y9TVMGg

Re: Building arbitrary Life patterns in 15 gliders

#98

Post by galaxyLogic »

dvgrn wrote: post #68
galaxyLogic wrote: post #52

Earlier quoted context omitted.

Very interesting. A biological cell is a 3-D self-replicating pattern (or is it 2-D rather?). Does GoL give us some insight into the nature of biological cells?

Definitely! It's hard to summarize that insight in any kind of concise way, though ... The Game of Life universe seems a bit too "fragile" to allow for the kind of emergent complexity that real-world physics supports. We can build self-constructing things like the https://conwaylife.com/wiki/0E0P_metacell , but if anything gets slightly out of place, the usual result is a truly horrific catastrophic explosion. Conway…

Fascinating

Re: Building arbitrary Life patterns in 15 gliders

#99

Post by rotexo »

As a biologist with nearly no physics knowledge, this sort of work seems to have more in common with setting up quantum computers than it does with thinking about self-replication in living organisms, at least in terms of the lack of robustness to environmental noise. Maybe that is just overly metaphorical thinking on my part.

Re: Building arbitrary Life patterns in 15 gliders

#100

Post by nneonneo »

rotexo wrote: post #99

As a biologist with nearly no physics knowledge, this sort of work seems to have more in common with setting up quantum computers than it does with thinking about self-replication in living organisms, at least in terms of the lack of robustness to environmental noise. Maybe that is just overly metaphorical thinking on my part.

It’s mathematics and computer science, not biology. Nobody is claiming that a setup requiring 2^1500000 units of space to run is anywhere near a realistic simulation of biological processes :)

Nevertheless, it’s a fantastic example of how simple rules can give rise to complex systems.

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