Meta-meta-blinker

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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calcyman
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Meta-meta-blinker

Post by 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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mmblinker.zip
Meta-meta-blinker
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What do you do with ill crystallographers? Take them to the mono-clinic!

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biggiemac
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Re: Meta-meta-blinker

Post by 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.
Physics: sophistication from simplicity.

Saka
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Re: Meta-meta-blinker

Post by Saka » December 16th, 2016, 2:59 am

I've always dreamed of this...
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

muzik
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Re: Meta-meta-blinker

Post by muzik » December 16th, 2016, 4:21 am

Here come the YouTube views.


...assuming I had a high enough quality recording software.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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calcyman
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Re: Meta-meta-blinker

Post by 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)?
What do you do with ill crystallographers? Take them to the mono-clinic!

Saka
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Re: Meta-meta-blinker

Post by Saka » December 16th, 2016, 6:15 am

The $1000 Question:
How meta can we go?
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

muzik
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Re: Meta-meta-blinker

Post by 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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Saka
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Re: Meta-meta-blinker

Post by 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)*
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

David
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Re: Meta-meta-blinker

Post by 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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muzik
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Re: Meta-meta-blinker

Post by 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).
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: Meta-meta-blinker

Post by 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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biggiemac
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Re: Meta-meta-blinker

Post by 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.
Physics: sophistication from simplicity.

NoLongerBreathedIn
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Re: Meta-meta-blinker

Post by 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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calcyman
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Re: Meta-meta-blinker

Post by 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.
What do you do with ill crystallographers? Take them to the mono-clinic!

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Re: Meta-meta-blinker

Post by 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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calcyman
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Re: Meta-meta-blinker

Post by 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.)
What do you do with ill crystallographers? Take them to the mono-clinic!

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Re: Meta-meta-blinker

Post by 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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calcyman
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Re: Meta-meta-blinker

Post by 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).
What do you do with ill crystallographers? Take them to the mono-clinic!

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Scorbie
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Re: Meta-meta-blinker

Post by 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...
Best wishes to you, Scorbie

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Re: Meta-meta-blinker

Post by 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

Post by 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

Post by gameoflifemaniac » March 5th, 2017, 3:28 am

This is completely off-topic!
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...

Saka
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Re: Meta-meta-blinker

Post by Saka » March 5th, 2017, 7:16 am

gameoflifemaniac wrote:This is completely off-topic!
Your post is off topic to lel
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

idonteven
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Re: Meta-meta-blinker

Post by 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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calcyman
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Re: Meta-meta-blinker

Post by 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.
What do you do with ill crystallographers? Take them to the mono-clinic!

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