Meta-meta-blinker
Meta-meta-blinker
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.
- Attachments
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- mmblinker.zip
- Meta-meta-blinker
- (186.08 KiB) Downloaded 1152 times
What do you do with ill crystallographers? Take them to the mono-clinic!
Re: Meta-meta-blinker
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.
Re: Meta-meta-blinker
I've always dreamed of this...
Re: Meta-meta-blinker
Here come the YouTube views.
...assuming I had a high enough quality recording software.
...assuming I had a high enough quality recording software.
Help wanted: How can we accurately notate any 1D replicator?
Re: Meta-meta-blinker
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)?muzik wrote:Here come the YouTube views.
...assuming I had a high enough quality recording software.
What do you do with ill crystallographers? Take them to the mono-clinic!
Re: Meta-meta-blinker
The $1000 Question:
How meta can we go?
How meta can we go?
Re: Meta-meta-blinker
Kindly ask the government or some other organisations with extremely hi-tech computer technology if you can borrow theirs.Saka wrote:The $1000 Question:
How meta can we go?
Help wanted: How can we accurately notate any 1D replicator?
Re: Meta-meta-blinker
Me: Hey NASA can u give us one of ur cool quantum supercomputersmuzik wrote:Kindly ask the government or some other organisations with extremely hi-tech computer technology if you can borrow theirs.Saka wrote:The $1000 Question:
How meta can we go?
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)*
Re: Meta-meta-blinker
Is B3/S23 really that omniperiodic(or, should I say, "omnivelocital")?Saka wrote: *Finds 7271c/1839281729 ship (Is this 7271c/1839281729 spaceship known? There may be bugs with zfind)*
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.
Re: Meta-meta-blinker
There are no c ships, so no (unless you only count stuff below and including c/2).David wrote:Is B3/S23 really that omniperiodic(or, should I say, "omnivelocital")?Saka wrote: *Finds 7271c/1839281729 ship (Is this 7271c/1839281729 spaceship known? There may be bugs with zfind)*
Help wanted: How can we accurately notate any 1D replicator?
Re: Meta-meta-blinker
The formal definition for "omnivelocital" would be:muzik wrote:There are no c ships, so no (unless you only count stuff below and including c/2).
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".
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.
Re: Meta-meta-blinker
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.
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Re: Meta-meta-blinker
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.
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.
Re: Meta-meta-blinker
I agree; that order of quantifiers makes much more sense to me. It's equivalent to the following definition: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.
"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."
The choice of norm doesn't affect the definition of omnivelocital since all norms on R^2 are Lipschitz-equivalent.Note that this is speed less than x in l^∞ norm, not l^1 norm usually used for 23/3, because that's easier.
What do you do with ill crystallographers? Take them to the mono-clinic!
Re: Meta-meta-blinker
Err... Why open?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."
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.
Re: Meta-meta-blinker
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.)David wrote:Err... Why open?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."
What do you do with ill crystallographers? Take them to the mono-clinic!
Re: Meta-meta-blinker
Why not the border?? Also, any subset of Q² cannot be an open set, except the empty set.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.)
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.
Re: Meta-meta-blinker
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.David wrote:Why not the border?? Also, any subset of Q² cannot be an open set, except the empty set.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.)
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!
Re: Meta-meta-blinker
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: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.
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...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).
Re: Meta-meta-blinker
Define "near" in R^2, and then define "near" in Q^2 (bogus terms, HTH) Look up for T^2 property.Scorbie wrote:...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...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).
(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
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.
- gameoflifemaniac
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Re: Meta-meta-blinker
This is completely off-topic!
I was so socially awkward in the past and it will haunt me for the rest of my life.
Code: Select all
b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$
4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!
Re: Meta-meta-blinker
Your post is off topic to lelgameoflifemaniac wrote:This is completely off-topic!
Re: Meta-meta-blinker
I tried doing this with the 'metafier' script and golly just exploded and said 'no memory'.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.
Also, sorry for the inactivity. I have a lot of homework. :p
LOVE IS LOVE
LIFE IS LIFE
CRUNCHYROLL IS CANCER
LIFE IS LIFE
CRUNCHYROLL IS CANCER
Re: Meta-meta-blinker
That's why you can't build something of this scale with metafier.py.idonteven wrote:I tried doing this with the 'metafier' script and golly just exploded and said 'no memory'.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.
Also, sorry for the inactivity. I have a lot of homework. :p
What do you do with ill crystallographers? Take them to the mono-clinic!