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Meta-meta-blinker

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Meta-meta-blinker

Postby calcyman » December 15th, 2016, 7:55 pm

Attached is a blinker made of copies of Brice Due's OTCA-metapixel, which are themselves made of OTCA-metapixels. Consequently, the period of this pattern is 2496135168; Golly can run an entire period over the course of a day at a step size of 8^5.
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Re: Meta-meta-blinker

Postby biggiemac » December 15th, 2016, 8:12 pm

It's a bit disappointing that the visual difference between "off" and "on" only persists to the first meta. It is still very cool to have an explicit realization of meta-meta-OTCA technology.
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Re: Meta-meta-blinker

Postby Saka » December 16th, 2016, 2:59 am

I've always dreamed of this...
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Re: Meta-meta-blinker

Postby muzik » December 16th, 2016, 4:21 am

Here come the YouTube views.


...assuming I had a high enough quality recording software.
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Re: Meta-meta-blinker

Postby calcyman » December 16th, 2016, 6:07 am

muzik wrote:Here come the YouTube views.


...assuming I had a high enough quality recording software.


Presumably this would be better rendered in something other than Golly, so that you can see which meta-metacells are on and off (cf. biggiemac's comment)?
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Re: Meta-meta-blinker

Postby Saka » December 16th, 2016, 6:15 am

The $1000 Question:
How meta can we go?
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Re: Meta-meta-blinker

Postby muzik » December 16th, 2016, 7:02 am

Saka wrote:The $1000 Question:
How meta can we go?

Kindly ask the government or some other organisations with extremely hi-tech computer technology if you can borrow theirs.
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Re: Meta-meta-blinker

Postby Saka » December 16th, 2016, 8:21 pm

muzik wrote:
Saka wrote:The $1000 Question:
How meta can we go?

Kindly ask the government or some other organisations with extremely hi-tech computer technology if you can borrow theirs.

Me: Hey NASA can u give us one of ur cool quantum supercomputers
NASA: Um, no, we can't do that. What for?
Me: Game of Life
NASA: Err
*Conway magically appears*
Conway: Thou shall giveth them thy supercomputer!
NASA: You can use Go boards.
*Ghost Martin Gardner appears*
Martin Gardner: Giveth them thy supercomputer!
NASA: Ok ok fine.
|Doot doo dooot! Quest completed! Obtained supercomputer!|
*Finds 7271c/1839281729 ship (Is this 7271c/1839281729 spaceship known? There may be bugs with zfind)*
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Re: Meta-meta-blinker

Postby David » December 17th, 2016, 7:11 am

Saka wrote:*Finds 7271c/1839281729 ship (Is this 7271c/1839281729 spaceship known? There may be bugs with zfind)*

Is B3/S23 really that omniperiodic(or, should I say, "omnivelocital")?
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Re: Meta-meta-blinker

Postby muzik » December 17th, 2016, 9:00 am

David wrote:
Saka wrote:*Finds 7271c/1839281729 ship (Is this 7271c/1839281729 spaceship known? There may be bugs with zfind)*

Is B3/S23 really that omniperiodic(or, should I say, "omnivelocital")?

There are no c ships, so no (unless you only count stuff below and including c/2).
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Re: Meta-meta-blinker

Postby David » December 17th, 2016, 9:22 am

muzik wrote:There are no c ships, so no (unless you only count stuff below and including c/2).

The formal definition for "omnivelocital" would be:

For a CA and any coprime integers a and b, if there exists a positive real number x that for any irreducible positive rational number less than or equal to x, n/p, spaceship with velocity (na, nb)c/p exists, we say that that CA is "omnivelocital".
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Re: Meta-meta-blinker

Postby biggiemac » December 17th, 2016, 3:11 pm

I think Gemini has proven omnivelocity of CGoL for a maximum speed of about 0.002c. I had to make sure that was consistent with your definition but now that I actually get it I think it's been done.
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Re: Meta-meta-blinker

Postby NoLongerBreathedIn » December 18th, 2016, 5:20 pm

I prefer the following definition of omnivelocitality:
CA C is omnivelocital if there is a real x s.t. for all a,b,p (a≥b, a/p<x, a,b,p coprime), there is an n such that there is a spaceship with period and speed (an, bn)c/pn.
Note that this is speed less than x in l^∞ norm, not l^1 norm usually used for 23/3, because that's easier.
For l^1 norm, we want (a+b)/p<x.
l^y norm? a^n+b^n<p^nx^n.
I don't know what the fastest speed in all directions for generic B3 rules is, because it's c/3 diagonal and c/2 orthogonal.
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Re: Meta-meta-blinker

Postby calcyman » December 19th, 2016, 5:58 am

NoLongerBreathedIn wrote:I prefer the following definition of omnivelocitality:
CA C is omnivelocital if there is a real x s.t. for all a,b,p (a≥b, a/p<x, a,b,p coprime), there is an n such that there is a spaceship with period and speed (an, bn)c/pn.


I agree; that order of quantifiers makes much more sense to me. It's equivalent to the following definition:

"A CA is omnivelocital if there is an open set U in Q^2 such that (0, 0) is in U and for every (a, b) in U, there is a spaceship with velocity (a, b)/c."


Note that this is speed less than x in l^∞ norm, not l^1 norm usually used for 23/3, because that's easier.


The choice of norm doesn't affect the definition of omnivelocital since all norms on R^2 are Lipschitz-equivalent.
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Re: Meta-meta-blinker

Postby David » December 19th, 2016, 9:28 am

calcyman wrote:"A CA is omnivelocital if there is an open set U in Q^2 such that (0, 0) is in U and for every (a, b) in U, there is a spaceship with velocity (a, b)/c."

Err... Why open?
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Re: Meta-meta-blinker

Postby calcyman » December 19th, 2016, 10:03 am

David wrote:
calcyman wrote:"A CA is omnivelocital if there is an open set U in Q^2 such that (0, 0) is in U and for every (a, b) in U, there is a spaceship with velocity (a, b)/c."

Err... Why open?


So that it contains a ball around the origin of some non-zero radius. (The two are clearly equivalent; just take the interior of your ball-containing set.)
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Re: Meta-meta-blinker

Postby David » December 19th, 2016, 7:02 pm

calcyman wrote:So that it contains a ball around the origin of some non-zero radius. (The two are clearly equivalent; just take the interior of your ball-containing set.)

Why not the border?? Also, any subset of Q² cannot be an open set, except the empty set.
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Re: Meta-meta-blinker

Postby calcyman » December 19th, 2016, 9:05 pm

David wrote:
calcyman wrote:So that it contains a ball around the origin of some non-zero radius. (The two are clearly equivalent; just take the interior of your ball-containing set.)

Why not the border?? Also, any subset of Q² cannot be an open set, except the empty set.


1. If U contains an open ball, then it also contains a non-trivial closed ball, and vice-versa. So requiring a border again has no effect on the definition.

2. Completely wrong. If U is an open subset of R^2, then the intersection of U with Q^2 is an open subset of Q^2 (that's basically how the subspace topology is defined).
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Re: Meta-meta-blinker

Postby Scorbie » December 20th, 2016, 9:43 am

calcyman wrote:1. If U contains an open ball, then it also contains a non-trivial closed ball, and vice-versa. So requiring a border again has no effect on the definition.
Hmm... But it might be a little important for specifying records (i.e. is the current status of gemini kc or kc-ε? (k is about 0.002 according to biggiemac))
calcyman wrote:2. Completely wrong. If U is an open subset of R^2, then the intersection of U with Q^2 is an open subset of Q^2 (that's basically how the subspace topology is defined).
Interesting. So that's how you define topology... I've never thought of such a concept as every point of Q^2 is seperated from each other...
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Re: Meta-meta-blinker

Postby Naszvadi » December 22nd, 2016, 6:05 pm

Scorbie wrote:...
calcyman wrote:2. Completely wrong. If U is an open subset of R^2, then the intersection of U with Q^2 is an open subset of Q^2 (that's basically how the subspace topology is defined).
Interesting. So that's how you define topology... I've never thought of such a concept as every point of Q^2 is seperated from each other...


Define "near" in R^2, and then define "near" in Q^2 (bogus terms, HTH) Look up for T^2 property.

(Theorem: T^n spaces' product is T^n space, if n is 1, 2 or 3. There is a counterexample for n==4)
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Re: Meta-meta-blinker

Postby Sphenocorona » December 24th, 2016, 7:04 pm

This discussion reminds me of a set of classifications based around the same idea of 'omni-velocity' rules that I had posted here earlier this year. Those classifications do have one drawback compared to the one here, which is that any rule with lightspeed spaceships is extremely unlikely to even achieve class 4.
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Re: Meta-meta-blinker

Postby gameoflifemaniac » March 5th, 2017, 3:28 am

This is completely off-topic!
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Re: Meta-meta-blinker

Postby Saka » March 5th, 2017, 7:16 am

gameoflifemaniac wrote:This is completely off-topic!

Your post is off topic to lel
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Re: Meta-meta-blinker

Postby idonteven » March 6th, 2017, 10:43 am

calcyman wrote:Attached is a blinker made of copies of Brice Due's OTCA-metapixel, which are themselves made of OTCA-metapixels. Consequently, the period of this pattern is 2496135168; Golly can run an entire period over the course of a day at a step size of 8^5.

I tried doing this with the 'metafier' script and golly just exploded and said 'no memory'.
Also, sorry for the inactivity. I have a lot of homework. :p
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Re: Meta-meta-blinker

Postby calcyman » March 6th, 2017, 1:30 pm

idonteven wrote:
calcyman wrote:Attached is a blinker made of copies of Brice Due's OTCA-metapixel, which are themselves made of OTCA-metapixels. Consequently, the period of this pattern is 2496135168; Golly can run an entire period over the course of a day at a step size of 8^5.

I tried doing this with the 'metafier' script and golly just exploded and said 'no memory'.
Also, sorry for the inactivity. I have a lot of homework. :p


That's why you can't build something of this scale with metafier.py.
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