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Integer glider synthesi?

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Integer glider synthesi?

Postby Mandelbrot » April 2nd, 2018, 4:14 pm

Well, hey again guys. Sorry for not posting in like a week, I’m still pretty new to this, so new in fact that I still don't know how to upload soups to catalogue. So, even though I can’t make any major discoveries in patterns, I would at least like to spark some discussion about something that has been in the back of my mind for longer than it should have been. So, in the scripts section of golly, there is a script titled life-integer-gun30.py. When run, it sets the rule to B3/S23 (If it wasn’t already) and produces a long sequence of numbers. When the pattern is run, it creates some LWSSes and those LWSSes collide in a way that make a glider synthesis of a gosper glider gun. I was wondering lately if there was anything like this for other patterns, and if not, could it be made? (Sorry if my post is off-putting or embarrassing to you or me.)
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Re: Integer glider synthesi?

Postby gameoflifemaniac » April 2nd, 2018, 4:36 pm

Welcome to the forums! For such things go to 'Thread for basic questions'. It's unnecessary to create a new topic only for this question. But you can delete it (at least make it invisible)! Just delete your post after I delete mine. PM me so that I know you've read this post and I can delete it. If you do that, you will have a bigger chance that someone will answer that. But what you have done isn't bad at all, just a bit inappopriate. Sorry if this post is too long.
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Re: Integer glider synthesi?

Postby A for awesome » April 2nd, 2018, 4:41 pm

gameoflifemaniac wrote:Welcome to the forums! For such things go to 'Thread for basic questions'. It's unnecessary to create a new topic only for this question. But you can delete it (at least make it invisible)! Just delete your post after I delete mine. PM me so that I know you've read this post and I can delete it. If you do that, you will have a bigger chance that someone will answer that. But what you have done isn't bad at all, just a bit inappopriate. Sorry if this post is too long.

I'm not sure that's precisely accurate — yes, that thread is for basic questions, but generally basic questions outside of that thread have been fairly well received, especially by new users who may not know about that thread or its intended purpose. I'd say keep this thread, it's fine.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Integer glider synthesi?

Postby gameoflifemaniac » April 2nd, 2018, 4:46 pm

A for awesome wrote:
gameoflifemaniac wrote:Welcome to the forums! For such things go to 'Thread for basic questions'. It's unnecessary to create a new topic only for this question. But you can delete it (at least make it invisible)! Just delete your post after I delete mine. PM me so that I know you've read this post and I can delete it. If you do that, you will have a bigger chance that someone will answer that. But what you have done isn't bad at all, just a bit inappopriate. Sorry if this post is too long.

I'm not sure that's precisely accurate — yes, that thread is for basic questions, but generally basic questions outside of that thread have been fairly well received, especially by new users who may not know about that thread or its intended purpose. I'd say keep this thread, it's fine.

I wrote:Just delete your post after I delete mine.

Never mind. Btw, is it never mind or nevermind?
And there's a typo in the title.
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Re: Integer glider synthesi?

Postby 77topaz » April 2nd, 2018, 4:58 pm

Actually on the topic of this thread, I'm not sure what your question actually is. Are you asking whether LWSS syntheses (that's the correct pluralisation, by the way) also exist for other patterns?
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Re: Integer glider synthesi?

Postby dvgrn » April 2nd, 2018, 5:03 pm

Mandelbrot wrote:So, in the scripts section of golly, there is a script titled life-integer-gun30.py. When run, it sets the rule to B3/S23 (If it wasn’t already) and produces a long sequence of numbers. When the pattern is run, it creates some LWSSes and those LWSSes collide in a way that make a glider synthesis of a gosper glider gun. I was wondering lately if there was anything like this for other patterns, and if not, could it be made?

Yes and no... this was originally an investigation by Dean Hickerson and Eric Angelini, back in early 2007. Eric's page on "Life integers" is now apparently only available on the Wayback Machine.

Dean's page on Life integers is still available, and see also Golly's pattern collection:
Patterns/Life/Syntheses/life-integer-constructions.rle

As far as building other objects with the same technique: it can be proven fairly easily nowadays that there is a Life integer that will evolve into every known glider-constructible object, from a blinker to a Gemini spaceship. In fact an unlimited number of successively larger integers can be found that produce each object.

Finding the smallest such integer for a given object is a highly non-trivial problem, but finding some integer for a particular object isn't too terribly hard.

It's actually within reach now to write a script that takes a glider construction recipe as input -- i.e., up to four salvos of gliders converging on a point -- and automatically converts it into a Life integer that produces the same result.

The script would be somewhat painful to write, which is why no one has done it yet -- but it's definitely doable in practice, not just theoretically.

That being said, the Gosper glider gun is currently the most complicated thing that has been built with Life integers, as far as I know -- especially using that technique of intersecting 90-degree streams of gliders built by colliding *WSSes.
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