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Building arbitrary Life patterns in 15 gliders

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Re: Building arbitrary Life patterns in 15 gliders

#41

Post by dvgrn »

biggiemac42 wrote: post #27
anderskaseorg wrote: post #7

Earlier quoted context omitted.

There’s no “larger glider”. The name “glider” refers to a single specific pattern of five cells. https://en.wikipedia.org/wiki/Glider_(Conway%27s_Life)

LMAO I found outdated info on that wikipedia page, in the best way. "Some patterns require a very large number (sometimes hundreds) of glider collisions"

Ha -- when was that written?... Let's see, the original form of the statement showed up in 2012: "Some patterns require a very large number (scores, even hundreds) of glider collisions..."

At that time Andrew Wade had already created the self-constructing Gemini spaceship, which needed 173449 gliders to build ( https://conwaylife.com/wiki/Glider_synthesis#Spaceship_synth... ). The recipe could have been reworked to be a little cheaper, but nobody bothered at the time -- and now it can be done in fifteen gliders instead.

If you want to see the construction happening, I'd definitely recommend the old Gemini recipe over an RCT-based one, though! RCT cuts down the cost in gliders to a minimum, but at a terrible cost in the time you have to wait around to see the completed object.

Re: Building arbitrary Life patterns in 15 gliders

#42

Post by enkid »

OscarCunningham wrote: post #40
enkid wrote: post #38

Earlier quoted context omitted.

21 cells would be a 3 by 7?

Gardens of Eden can be arbitrary patterns, whereas only the 21-cell still lifes are known to be constructible.

Ok, but what do you mean by a "still life" of 21 cells? Is that a rectangle in a larger field or is it an arbitrary set of cells?

Re: Building arbitrary Life patterns in 15 gliders

#43

Post by dvgrn »

bewresu wrote: post #36
ivoras wrote: post #34

Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encoding the time at which a certain pattern (a glider) appears where it's needed. In a rigid system like the GoL, we can't trade space with time easily, since everything happens at a constant speed, but it makes one wonder...

...if there's a GoL version where time varies somehow¹ with something² ¹ directly? ² amount of activity? mass?

There have been a lot of GoL variants over the years, but I don't remember running into any attempts to vary the speed of evolution in different locations on the same grid.

The idea that all neighbors move to the next tick simultaneously is a fundamental assumption in cellular automata in general. If you try changing that, the optimizations that allow us to simulate CAs at any kind of reasonable speed ... all stop working, pretty much. It's kind of painful even to think about.

Which means there are probably very interesting rules out there somewhere, where CAs run faster/slower depending on pattern density -- it's just going to be very tricky to explore that particular search space.

Re: Building arbitrary Life patterns in 15 gliders

#44

Post by Grustaf »

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?

Re: Building arbitrary Life patterns in 15 gliders

#45

Post by OscarCunningham »

enkid wrote: post #42
OscarCunningham wrote: post #40

Earlier quoted context omitted.

Gardens of Eden can be arbitrary patterns, whereas only the 21-cell still lifes are known to be constructible.

Ok, but what do you mean by a "still life" of 21 cells? Is that a rectangle in a larger field or is it an arbitrary set of cells?

A pattern with 21 live cells in any bounding box.

Re: Building arbitrary Life patterns in 15 gliders

#46

Post by enkid »

OscarCunningham wrote: post #45
enkid wrote: post #42

Earlier quoted context omitted.

Ok, but what do you mean by a "still life" of 21 cells? Is that a rectangle in a larger field or is it an arbitrary set of cells?

A pattern with 21 live cells in any bounding box.

Thanks for answering!

Re: Building arbitrary Life patterns in 15 gliders

#47

Post by kryptiskt »

Traubenfuchs wrote: post #16
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

How much of advanced GoL is intuition and genius you were born with and how much is math/logic anyone can learn with enough time?

I can recommend the recent book "Conway's Game of Life: Mathematics and Construction" (downloadable free at https://conwaylife.com/book/), it starts gently and builds up to these kind of constructions (minus what has been discovered in the last year or so).

Re: Building arbitrary Life patterns in 15 gliders

#48

Post by dvgrn »

biggiemac42 wrote: post #18
Traubenfuchs wrote: post #16

Earlier quoted context omitted.

How much of advanced GoL is intuition and genius you were born with and how much is math/logic anyone can learn with enough time?

Definitely worth trying to learn! As with most topics, it starts out seeming hard to grasp, and then you start naming things and recognizing them. What looks like jargon to an outsider is just a compressed way of communicating. The people in the community are smart and tend to compress their ideas really far which makes the jargon even more extreme. Advanced gol is just getting past that first hurdle of understanding…

I think the biggest prerequisite for getting good at "advanced GoL" is just an unreasonable amount of patience.

Probably I'm a good case in point. I'm definitely not a particularly clever mathematician, but it seems like it's possible to understand any new Life technology just by tinkering with the pieces for long enough.

If anyone wants to follow along with that kind of learning process, just start working through the Life textbook that kryptiskt mentioned. (Full disclosure, I'm one of the authors.)

Re: Building arbitrary Life patterns in 15 gliders

#49

Post by andrepd »

ivoras wrote: post #34

Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encoding the time at which a certain pattern (a glider) appears where it's needed. In a rigid system like the GoL, we can't trade space with time easily, since everything happens at a constant speed, but it makes one wonder...

How does it "touch on relativity of space and time"?

Re: Building arbitrary Life patterns in 15 gliders

#50

Post by [deleted] »

ivoras wrote: post #34

Interestingly enough, the concept of placing gliders at a distance away seems to touch on the relativity of space and time. Here, with space, we are also encoding the time at which a certain pattern (a glider) appears where it's needed. In a rigid system like the GoL, we can't trade space with time easily, since everything happens at a constant speed, but it makes one wonder...

[deleted]
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