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Spaceship speed limits

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Spaceship speed limits

Postby Macbi » June 6th, 2009, 11:39 am

Is the proof that spaceships can't go faster than c/2 on the net somewhere? I can't find it.
Last edited by Macbi on April 24th, 2010, 6:06 am, edited 1 time in total.
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B34578 is stable but B34578/S2 dies out much more.
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Re: Game of Life Links

Postby dvgrn » June 6th, 2009, 1:39 pm

> I[s] the proof that spaceships can't go faster than c/2 on the net somewhere?

You're right, the actual c/2 and c/4 speed limit proofs seem harder to find than they should be. Here's something written by John Conway on 24 Mar 1994, summarizing the original result from much longer ago -- the proofs are mentioned but not quoted in the original October 1970 Mathematical Games article (http://www.ibiblio.org/lifepatterns/october1970.html).

I've reformatted the text slightly... what should I use instead of "code" tags to get a fixed-width font, anyway?

---begin quote---

JHC> Here's my old proof of the speed limit results:

Suppose we are initially below the diagonal line abcde... in the figure I'll soon draw, at time 0. Then for x to be born at time 2, we'd need u and v to have been born at time 1, and c to be alive at time 1.

However, for u and v to be born at time 1, we'd need b, m, c, n, d all to be alive at time 0, and that means that c would die of overcrowding, so wouldn't be alive at time 1.

        a
         bux
         mcv
          nd
            e
             f

This shows that if a configuration is behind a diagonal line at time 0, it's necessarily behind the next such line at time 1, and so on, which restricts the speed in diagonal directions to c/4.

If you're below two diagonal lines at time 0:

               m
              l n
             k   o
            j     p
           i       q
          h         r
              ...

then you're below the ones just above them at time 1. So this "bow shock" can travel vertically at at most c/2.

The glider attains c/4 in diagonal directions, and the spaceships attain c/2 in orthogonal ones, so they move as fast as is possible for finite configurations.

---end quote---
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Re: Spaceship speed limits

Postby Elithrion » June 6th, 2009, 3:43 pm

Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.
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Re: Spaceship speed limits

Postby Nathaniel » June 6th, 2009, 4:19 pm

Elithrion wrote:Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.


I was wondering the same thing. The proof only seems to rely on the fact that "3" is a birth condition, "0", "1" and "2" are not a birth conditions, and "4" is not a survival condition, so any rule of the form B3(45678)/S(01235678), where numbers in brackets are optional, should have those upper bounds (and maybe tighter upper bounds in some cases as well).

Clearly you can't go faster than c orthogonally, but for some reason c/3 seems to be the magically upper limit for diagonal spaceships in weird rules (example), and I'm not sure why.

Edit: Sorry, c/2 seems to be the upper diagonal limit for arbitrary rules, which seems like it shouldn't be hard to prove. c/3 seems to be the upper diagonal limit for rules without "2" in the birth list, and I'm not sure why *that* is.
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Re: Spaceship speed limits

Postby dvgrn » June 7th, 2009, 12:45 pm

Elithrion wrote:Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.


And if you want to dodge the spaceship speed limit even in plain old Conway's Life, all you have to do is relax the condition about travelling through a vacuum. The 2c/3 and lightspeed "negative spaceships" through an infinite stripes agar were a wonderful find (see the bottom of Gabriel Nivasch's lightspeed signals page -- RLE link).

I wonder how many other kinds of "ocean" in Conway's Life it will turn out to be possible to swim through...? There are probably a number of other surprises out there on the same order as the 2c/3-to-anywhere-in-the-Universe bombshell.
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Re: Spaceship speed limits

Postby H. V. McIntosh » January 7th, 2010, 9:30 pm

Macbi wrote:If the proof that spaceships can't go faster than c/2 on the net somewhere? I can't find it.

By now, that's been answered, both here and via Google. However, I have a related question, for which searching doesn't reveal much of anything: In the Wiki "Rotor" entry we find
Under the standard Conway rules any rotor cell must be adjacent to another rotor cell., but ... .
Lexicon says it is "easy to see," but not for me. Offhand it would seem that one would need to scan all 32M 5x5 neighborhoods to find which ones had a 3x3 central core in which both the center cell and at least one of the others did not change.

In a vacuum, a single live cell can change without any other change. But it's not an oscillator, so that must be important. A beacon or the test tube babies have coupled adjacent pairs, which works well enough. Babbling brooks &c depend on this. Does someone have either a reference or an explanation?
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Re: Spaceship speed limits

Postby calcyman » January 8th, 2010, 11:43 am

Lexicon says it is "easy to see," but not for me.


Every rotor cell is alive in some phase(s) of the oscillator, and dead in others. Now consider a dead cell directly before it becomes alive. It must, by definition, be surrounded by three live cells. If these cells are stator cells, not rotor cells, then the isolated rotor cell will continue to have three live neighbours permanently. Such a cell is a stator cell, not a rotor cell. Reductio ad absurdum.
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Re: Spaceship speed limits

Postby H. V. McIntosh » January 12th, 2010, 1:26 am

calcyman wrote: Reductio ad absurdum.
So it seems that the oscillator part is essential, otherwise we never return to that first cell. Actually, it seems that I misread or misunderstood the whole definition, since I expected an immediate reaction. Which one has, when the period is 2. However the connected string doesn't have to go very far, as in the beacon, test tube babies, and so on. That is probably why there are so few babbling brooks, although there do seem to be oscillators with lots of cells which are pure rotor.

Anyway I'm glad to have that cleared up. In a way, it's just common sense, since a changed cell implies a changed neighborhood unless you have a rule in which the same neighborhood just bounces its cell back and forth.
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Re: Spaceship speed limits

Postby H. V. McIntosh » April 5th, 2010, 3:04 am

So, space ships have their speed limits, but extended structures can behave differently, especially with respect to superluminal movement. What if the structure is not extended? A recent example was the reasonable explanation in the LifeWiki that the stargate was an optical illusion, but that leads to the interesting question of whether the stargate needs a steady stream of space ships to generate the boost, or if it can be done on demand? Probably not because that would imply rapid movement of information, but it does raise the question of the extent to which widely separated activities can be considered to be correlated.

In that direction, I have been wondering about the electric fence, which absorbs and releases ants from a finite stream. Either edge could be removed to obtain matching wicks, but there are further possibilities.

1) trivially, two separated terminators could be used to create a gap in the ant stream, absorb two oppositely directed ant streams or conversely to emit them. Could these two separate terminators be coalesced into a single object?

2) the ant stream is symmetric about its axis of propagation, but the terminators are not. Is there any reason why they couldn't be? As it stands, each has a distinct mirror image which would function equally well; the choice between them may be historical, or it could be just to adjust the size of the bounding box.

3) There are varieties of ants. Does each have a corresponding terminator, again subject to the foregoing questions.

4) can an ant stream be turned 90 degrees, preferably by setting matching terminators at right angles? It is hard to turn space ships, probably equally so for ants.

All this probably calls for a search program, of which I do not have one handy.
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Re: Spaceship speed limits

Postby PM 2Ring » April 5th, 2010, 8:23 am

A recent example was the reasonable explanation in the LifeWiki that the stargate was an optical illusion, but that leads to the interesting question of whether the stargate needs a steady stream of space ships to generate the boost, or if it can be done on demand?
The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. A glider or (other) space ship accelerator that used stable technology and had a fast recovery time would be very interesting!
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Re: Spaceship speed limits

Postby H. V. McIntosh » April 5th, 2010, 11:57 pm

PM 2Ring wrote:..... The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. .....

Yes, this much can be found via Internet, and concretely, in the LifeWiki. However, I wonder if this description is truly worthy of the reference source which we are trying to work up. For example, without going after Golly or some similar program, I still don't know whether "in synch with the stargate" means that the glider stream must be continuous, or whether it can have gaps. Presumably the latter, since the fast forward mechanism ignores a missing space ship, while promoting one which is physically present. It would be reassuring to have this spelled out, particularly given the complexity of the stargate. I mean, as written the sentence seems to be totally correct, but the problem is really to get the reader to understand and believe it.

As for the complexity, why can't a force field simply lay in wait for a space ship, and kick
it along if one shows up (with all due respect for the phase)? Presumably a stargate has to set up several force field generators to handle more than one at a time, leading to the
question of designing one to handle several at one go. I've been looking at the stargate image trying to pick out the individual generators, but there are a lot of them and the resolution isn't wonderful.

Assuming for the moment that the gate will handle sparse streams, we have something like the situation in experimental quantum mechanics wherein a diffraction experiment is performed at such a low density that only one electron is loose in the video camera at any one time. Nevertheless, by waiting, a perfectly convincing diffraction pattern will evolve. Transferring this idea to Life, set up a sequence of stargates into which a single space ship is launched at a precise phase from a given place. Somewhat later look at the far end of
its track, to find that it has arrived somewhat sooner that predicted by the velocity of light. Or not; implying a transmission of information.

Somehow that seems to be a real effect, and not just an optical illusion.
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Re: Spaceship speed limits

Postby calcyman » April 6th, 2010, 5:13 am

Somehow that seems to be a real effect, and not just an optical illusion.



No, because the reactions cannot be compacted close enough together to propagate information faster than lightspeed. Indeed, it is simple to prove that information cannot travel at superluminal speeds, due to the fact that the rules of Life only update a cell based on its Moore-connected neighbours after one generation.

If you're still not convinced, then construct such a pattern for yourself. You'll find that it either functions below lightspeed, explodes, or otherwise detects the 'ghost' LWSSes as being actual ones, and emits a spaceship regardless of whether a spaceship actually entered the device.
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Re: Spaceship speed limits

Postby PM 2Ring » April 6th, 2010, 8:21 am

H. V. McIntosh wrote:
PM 2Ring wrote:..... The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. .....

Yes, this much can be found via Internet, and concretely, in the LifeWiki. However, I wonder if this description is truly worthy of the reference source which we are trying to work up. For example, without going after Golly or some similar program, I still don't know whether "in synch with the stargate" means that the glider stream must be continuous, or whether it can have gaps. Presumably the latter, since the fast forward mechanism ignores a missing space ship, while promoting one which is physically present. It would be reassuring to have this spelled out, particularly given the complexity of the stargate. I mean, as written the sentence seems to be totally correct, but the problem is really to get the reader to understand and believe it.

Yes, the LWSS stream can have gaps in it. For example, see here for a pattern I built last August, using a modified form of Calcyman's LWSS fanout device (LWSS duplicator). It feeds the fanout device with an intermittent stream of LWSSs and uses 4 copies of the stargate to accelerate the output LWSS stream to synchronize it vertically with the input LWSS stream.

It's not easy to describe complex patterns. It's hard to know what level of detail to go down to, and which reactions need to be explained in detail. Also, after working with a pattern for a while, the sub-patterns & reactions tend to seem obvious, and so one may not realize that they need explaining. But this is a topic for another thread. :)

As for the complexity, why can't a force field simply lay in wait for a space ship, and kick
it along if one shows up (with all due respect for the phase)? Presumably a stargate has to set up several force field generators to handle more than one at a time, leading to the
question of designing one to handle several at one go. I've been looking at the stargate image trying to pick out the individual generators, but there are a lot of them and the resolution isn't wonderful.

A new pair of force field reactions occur every 60 steps. Roughly speaking, the force field reaction eats a LWSS at its left end while synthesizing a new LWSS at its right. But if the LWSS at the left fails to appear, the LWSS on the right is killed by the sparks from the left.

While the whole stargate pattern may appear daunting at first glance, most of its bulk is in its glider guns. The forcefield reaction itself is remarkably compact in space & time:
Image
The output LWSS appears at step 6, the debris is clear by step 28 if the output LWSS escapes, or by step 39 if it gets destroyed.

Here are two copies of the forcefield in a row, as used in the stargate. Using two of them restores the LWSS phase.
x = 39, y = 18, rule = B3/S23
21bo5bobo$19bobo6b2o$20b2o6bo3$7bo6bo$8bo6b2o$2b2o2b3o5b2o$2ob2o$4o9bo
$b2o9b2o$12bobo4$37b2o$36b2o$38bo!

Somehow that seems to be a real effect, and not just an optical illusion.

Is it reality or an optical illusion? I'm still not sure. I shall have to build my own stargate tunnel & contemplate this question...

When I first saw the stargate, I just assumed it worked by magic. :) Although I was interested in Life in the early 1970s, much of its development passed me by, and when I discovered all the incredible patterns that had been built by the mid 90s, I was amazed and rather overwhelmed. I thought I'd never understand how things like glider gun puffers worked. And so I didn't delve into the details of these fancy patterns for several years. But eventually curiosity got the better of me, and I felt the desire to try & build some glider based circuits myself. I'm more comfortable with complex constructions these days, but I don't know if I really understand a lot of the reactions I use, I've just become more familiar with them. :)
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Re: Spaceship speed limits

Postby calcyman » April 6th, 2010, 11:39 am

Is it reality or an optical illusion? I'm still not sure. I shall have to build my own stargate tunnel & contemplate this question...



I can demonstrate the invalidity of the stargate reaction:


First, observe this pattern, which accelerates a LWSS at 15c/14, overtaking a lightspeed signal:

x = 430, y = 176, rule = B3/S23
bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbo$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3$12bo$$12bo$$12bo$$12bo$$12bo$$12bo255bo6bo$269bo6boo$12bo254b
3o5boo$$12bo244bo5bobo$255bobo6boo$12bo243boo6bo$245bo6bo$12bo233bo6b
oo$244b3o5boo$12bo$234bo5bobo$12bo219bobo6boo$233boo6bo$12bo209bo6bo$
223bo6boo$12bo208b3o5boo$$12bo198bo5bobo$209bobo6boo$12bo197boo6bo$
199bo6bo$12bo187bo6boo$198b3o5boo$12bo$188bo5bobo$12bo173bobo6boo$187b
oo6bo$12bo163bo6bo$177bo6boo$12bo162b3o5boo$$12bo152bo5bobo$163bobo6b
oo$12bo151boo6bo$153bo6bo$12bo141bo6boo$152b3o5boo$12bo$142bo5bobo$12b
o127bobo6boo$141boo6bo$12bo117bo6bo$131bo6boo$12bo116b3o5boo$$12bo106b
o5bobo$117bobo6boo$12bo105boo6bo$107bo6bo$12bo95bo6boo$106b3o5boo$12bo
$96bo5bobo$12bo81bobo6boo$95boo6bo$12bo71bo6bo$85bo6boo$12bo70b3o5boo
$$12bo60bo5bobo$71bobo6boo$12bo59boo6bo$61bo6bo$12bo49bo6boo$60b3o5boo
$12bo$50bo5bobo$12bo35bobo6boo$49boo6bo$12bo25bo6bo$39bo6boo$12bo24b3o
5boo$$12bo14bo5bobo$25bobo6boo$12bo13boo6bo$15bo6bo$16bo6boo$10boobb3o
5boo$8booboo$8b4o9bo$9boo9boo$20bobo$$39boo$38boo$40bo$58bo$57boo$57bo
bo$$76boo$75boo$77bo$95bo$94boo$94bobo$$113boo$112boo$114bo$132bo$131b
oo$131bobo$$150boo$149boo$151bo$169bo$168boo$168bobo$$187boo$186boo$
188bo$206bo$205boo$205bobo$$224boo$223boo$225bo$243bo$242boo$242bobo$$
261boo$260boo$262bo$280bo$279boo$279bobo$$298boo$297boo$299bo$317bo$
316boo$316bobo$$335boo$334boo$336bo$354bo$353boo$353bobo$$372boo$371b
oo$373bo$391bo$390boo$390bobo$$409boo$408boo$410bo$428bo$427boo$427bob
o!



That seems quite genuine at first, doesn't it? The stargate reaction _does_ accelerate the LWSS to a superluminal speed -- 15c/14.

Now delete the LWSS:

x = 430, y = 176, rule = B3/S23
bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbo$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3$12bo$$12bo$$12bo$$12bo$$12bo$$12bo255bo6bo$269bo6boo$12bo254b
3o5boo$$12bo244bo5bobo$255bobo6boo$12bo243boo6bo$245bo6bo$12bo233bo6b
oo$244b3o5boo$12bo$234bo5bobo$12bo219bobo6boo$233boo6bo$12bo209bo6bo$
223bo6boo$12bo208b3o5boo$$12bo198bo5bobo$209bobo6boo$12bo197boo6bo$
199bo6bo$12bo187bo6boo$198b3o5boo$12bo$188bo5bobo$12bo173bobo6boo$187b
oo6bo$12bo163bo6bo$177bo6boo$12bo162b3o5boo$$12bo152bo5bobo$163bobo6b
oo$12bo151boo6bo$153bo6bo$12bo141bo6boo$152b3o5boo$12bo$142bo5bobo$12b
o127bobo6boo$141boo6bo$12bo117bo6bo$131bo6boo$12bo116b3o5boo$$12bo106b
o5bobo$117bobo6boo$12bo105boo6bo$107bo6bo$12bo95bo6boo$106b3o5boo$12bo
$96bo5bobo$12bo81bobo6boo$95boo6bo$12bo71bo6bo$85bo6boo$12bo70b3o5boo
$$12bo60bo5bobo$71bobo6boo$12bo59boo6bo$61bo6bo$12bo49bo6boo$60b3o5boo
$12bo$50bo5bobo$12bo35bobo6boo$49boo6bo$12bo25bo6bo$39bo6boo$12bo24b3o
5boo$$12bo14bo5bobo$25bobo6boo$12bo13boo6bo$15bo6bo$16bo6boo$14b3o5boo
$$21bo$20boo$20bobo$$39boo$38boo$40bo$58bo$57boo$57bobo$$76boo$75boo$
77bo$95bo$94boo$94bobo$$113boo$112boo$114bo$132bo$131boo$131bobo$$150b
oo$149boo$151bo$169bo$168boo$168bobo$$187boo$186boo$188bo$206bo$205boo
$205bobo$$224boo$223boo$225bo$243bo$242boo$242bobo$$261boo$260boo$262b
o$280bo$279boo$279bobo$$298boo$297boo$299bo$317bo$316boo$316bobo$$335b
oo$334boo$336bo$354bo$353boo$353bobo$$372boo$371boo$373bo$391bo$390boo
$390bobo$$409boo$408boo$410bo$428bo$427boo$427bobo!


The right-hand-side of the pattern still receives the LWSS, even though it was not initially present. This is because the 4F reactions must be separated in order to work, at which point they become subluminal.


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Re: Spaceship speed limits

Postby PM 2Ring » April 7th, 2010, 3:41 am

I spent some time last night playing with patterns like the ones Calcyman posted above, but with enough separation to allow the reactions to work properly. I now agree that the stargate's fast forward reaction (FFR) is an optical illusion.

At step 6, the FFR produces a LWSS displaced 11 cells to the right of the input LWSS at step 0. This is the source of the apparent superluminal movement. However, the minimum repeat time (aka compression) of the FFR is 22 steps, and of course over the other 16 steps the LWSS moves the expected 8 cells. So during the 22 step cycle, the LWSS appears to move a total of 19 cells, yielding a mean speed of 19c/22 ~= 0.8636c, which is still a lot faster than the usual LWSS speed of 0.5c, but it's hardly superluminal. However, if we "cheat" & measure the speed over a 28 step period we get (11 + 8 + 11)c / (6 + 16 + 6) = 30c/28 ~= 1.0714c.

If we chain multiple copies of the FFR together, the mean speed reduces. If we use n copies, the best speed we can achieve is (19*n + 11)/(22*n + 6) , as illustrated in the following table:
0:  11/  6 = 1.833333    10:  201/ 226 = 0.889381   
1:  30/ 28 = 1.071429    20:  391/ 446 = 0.876682
2:  49/ 50 = 0.980000    30:  581/ 666 = 0.872372
3:  68/ 72 = 0.944444    40:  771/ 886 = 0.870203
4:  87/ 94 = 0.925532    50:  961/1106 = 0.868897
5: 106/116 = 0.913793    60: 1151/1326 = 0.868024
6: 125/138 = 0.905797    70: 1341/1546 = 0.867400
7: 144/160 = 0.900000    80: 1531/1766 = 0.866931
8: 163/182 = 0.895604    90: 1721/1986 = 0.866566
9: 182/204 = 0.892157   100: 1911/2206 = 0.866274
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Re: Spaceship speed limits

Postby H. V. McIntosh » April 7th, 2010, 10:29 pm

Still, although the velocity of light has not been exceeded, the space ships still seem to be moving along faster that c/2, namely 19/22 nds of c; probably explicable by the bulk of the stargate mechanism. Although a single jump is plausibly an illusion, the criterion of "how long does it take for the consequences of an event in one place to reach another?" still stands in contradiction to the properties of space ships, even though it does fall within the limits of causality. Probably the illusion results from our tendency to see whole patterns where they don't really exist; tracing the movement of individual bits probably doesn't move them as fast as the apparent single step jump calls for.

Actually, examining the fast forward construction, it seems that we basically have a three glider near synthesis of a light weight space ship. Interestingly, if it takes place just in front of an oncoming space ship, the cloud of trailing debris dissipates; approximately thirty generations are required. Otherwise the construction fails although, the space ship almost escapes. It would be interesting to know more about the search strategy via which it was discovered; also whether it could be applied to longer space ships. It would also be interesting to have more details of the glider syntheses at hand, since promoting such a reaction to a stargate evidently involves knowing the size of the debris cloud, whether more gliders are needed to kill it, and the required packing of all the glider sources involved.

As for the teleportation itself, there is an eating mechanism and a production mechanism at work. To obtain a causal coupling between them, we need to cover the distance between the head of the deceased and the tail of the newborn; the gap between head and tail then measures the jump which can be attributed to teleportation. Waiting for debris to settle affects the overall velocity, depending on how far the space ship has to move at its regular velocity before being hurled forward again.

That Wiki page is still a molestation - not only for the scale, but for locating the spaceships. For example, the gliders come in from both directions, so the space ships at the bottom of the figure must be for comparison, since they cannot be teleported. Also, I'm sorry if I don't think Java programs should be incorporated into text pages.
-hvm
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Re: Spaceship speed limits

Postby H. V. McIntosh » April 24th, 2010, 12:19 am

The illusion part of the fast forward force field sems to be settled, the teleportation's jump being related to the distance between the bow and the stern of the teleportee. Except for the stargate, which employs serial fields, there don't seem to be other instances of teleportation among the Life patterns, raising the question of whether there really are any other instances and if so, how many of them have been found? In other words:
1) can longer space ships or even flotillas be teleported?
2) can the teleportee be offset, rather than just skipping forward in the same trajectory?
3) can it be turned into an orthogonal course?
4) can it be reflected back by some distance?
5) are there other force fields?
-hvm
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Re: Spaceship speed limits

Postby H. V. McIntosh » May 5th, 2010, 2:03 am

I wrote: ..... 5) are there other force fields?
In a manner of speaking, conduits are also force fields; their action is probably not regarded as teleportation because the effects are not instantaneous. But then, neither is what we have been calling teleportation. Quoting from the LifeWiki,
A conduit is an arrangement of still lifes and/or oscillators that moves an active object to another location without themselves being permanently damaged. .....
We are only missing the gliders, but we are accepting the possibility of rotation, flipping, displacement, and transmutation; all of which were possibilities in the above query.

The conduit page in the Wiki could probably use some elaboration; it only asserts that there are sixteen elementary Herschel conduits. But
[*] Buckingham's list only contains eight, although
[*]images for them are provided. Presumably there is a
[*]calculus, or grammar for combining them

The complexity of this latter is probably why there are search programs, and that the results reported are only loosely assorted into families.
-hvm
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Re: Spaceship speed limits

Postby doccolinni » May 20th, 2010, 10:40 am

I'm sort of a new guy here, but I hope you won't mind me sharing my take on what the so-called Stargate actually does.

Whether the Stargate actually makes the LWSSes move faster than light or just creates an illusion of it is an irrelevant and in fact purely philosophical matter - the LWSS that hits the gliders from the left gets destroyed so although a new LWSS is created on the right one might say that that's a new LWSS and previous one is not there any more at all, but then again if an LWSS didn't hit the gliders from the left side the new LWSS wouldn't have been created on the right side at all so one might say that as the direct consequence of the "old" LWSS the "new" LWSS basically makes the old one live on... See, it's all just philosophical nonsense.

What's really important here are the information throughputs of a stream of LWSSes travelling regularly and with the aid of the Stargate. Let me explain what I'm talking about...

First of all, what's actually sneaky in that Stargate pattern lies down below - it's the regularly-travelling LWSSes that serve the purpose of comparing the regular travel of LWSSes to the one aided by the Stargate. A more fair comparison is actually provided by this pattern:

x = 155, y = 133, rule = B3/S23
25b2o85b2o$24bobo44bobo37bobo$10bo12b3o4b2o34bo4bo2bo35bo13bobo$5bo4b
4o8b3o4bo2b4o31b2o5b2o8bo16b2o7bo2bo6b2o2bo2bo$5bo5b4o8b3o4b2ob3o26b2o
8bo3b2o5bobo15b2o7bo8bobo5b2o$2o9bo2bo9bobo35b2o10b2o6bob2o25bobo3bo3b
o3bo3b2o4b2o$2o9b4o10b2o44bo2bo6b2ob2o10b2o14b2o2b2ob3o5b2o6b2o$10b4o
8bo48bobo8bob2o10b2o21b2o3bo2bo$10bo12bo59bobo20b2o16bobo$21b3o50bo9bo
21bo$34b2o19b2o16bo21b2o7bobo$5b2o28bo19bo17b3o19b3o6b2o4bo$5b2o28bobo
6b2o7bobo25bo15b2obo9bobo$36b3o5bobo6b2o24bobo4b3o8bo2bo9b2o$38b3o6bo
30bobo16b2obo$5bo32bo2bo2bo2bo29bo2bo7bo2b2o2b3o$4bobo32b2o6bo8bo21bob
o7bo3bo2b2o$3bo3bo8b3o25bobo9b3o7bo7b2o3bobo6bo2bo29b2o23b2o$3b5o10bo
25b2o13bo6bobo4bobo5bo8b2o11bo17bobo22bo$2b2o3b2o8bo40b2o6b2o5bo28bo
13b2o6bo11bobo5bobo$3b5o13bo30b2o18b2o28b3o7b2obo2bo2bo2bo10bo2bo5b2o$
4b3o12b3o31bo58b2o2b2o6bo9b2o12b2o$5bo12bo18bo6bo8bobo65bobo8b2o3bo10b
2o$18b2o18bo6b2o7b2o21b2o42b2o11b2o12b2o$9b2o25b3o5b2o15b2o13b4o11b2o
33bo8bo2bo10bo$8bobo4bo12b2o30b2ob2o10b2ob2o10b2ob2o29b2o10bobo9bobo$
10bo4bo11bobo31b4o11b2o13b4o21b2o7b2o21bobo$29bo32b2o28b2o22bo32bo$
106bo7bobo$13b2o3b2o79b2obo3b4o4b2o$14b5o4b2o68b2o2b2obobo4b4o35b2o3b
2o$15b3o4bo2bo66bobo2b2obob2o3bo2bo35bobobobo$16bo49bo24b3o8b2o3b4o6bo
bo27b5o$6b3o11bo43bobo15b2o6b3o8b2o3b4o7b2o29b3o$5bo3bo12bo42b2o15b2o
7b3o12bo11bo30bo$21bo70bobo$4bo5bo82b2o$4b2o3b2o41bo6bo83b2o$30b3o20bo
6b2o81bo$30bo20b3o5b2o50bo21bobo5bobo$7bo23bo77b2o22bo3bo3b2o$6bobo8b
3o90b2o5bo19bo8bobo$6bobo106b4o14bo4bo7b2o$6bo10bobo26bobo65bobob2o4bo
12bo9bo$6bo9b5o17b3o5bo3bo62bo2bob3o5b2obo3bo3bo$6bo2bo5b2o3b2o11b2o2b
o2bobo7bo42bo19b2obob2o5b4obo2bobo$7b2o6b2o3b2o9bo2bo2b2o7bo4bo41b3o
15b3ob4o6b2o2b2o19b3o$30bo19bo30bo14bo5bobo5bobo4bo31bo3bo$30bo10b3o2b
o3bo3b2o23bobo13b2o5b2o6bo29bo7bo5bo$18bo11bo15bobo5bobo23b2o7b2o12bo
5b2o27b2o9bo3bo$16b2o6b2o5bo2bo21bo33bo48b2o9b3o$23bobo7b2o21b2o32bobo
57b3o$15bo7bo43bo6bo16b2o4bo2bo26bo2bo$22b2o44bo6b2o19bo14b4o11bo$16bo
2bo46b3o5b2o20bo3bo10bo3bo10bo3bo$18b2o76b4o11bo14b4o20b2o$112bo2bo34b
2o$135b2o8bo$135bo2bo6bobo$130b2o2bo3bo7bobo4b2o$129b3o2b2o2bo7bo2bo3b
2o$119b2o5bob2o16bobo$96bo5bobo14b2o5bo2bo8b3o4bobo$94bobo6b2o21bob2o
15bo$95b2o6bo25b3o$130b2o2$82bo6bo$83bo6b2o$17b2o28b2o28b2o2b3o5b2o$
15b2ob2o25b2ob2o25b2ob2o$15b4o26b4o26b4o9bo$16b2o28b2o28b2o9b2o$87bobo
2$128b2o$128b2o$112b2o26b2o$111b2o27b2o$88bo24bo$88b3o$91bo51bo$90b2o
36b3o11bo$142bo$128bobo$127b5o$103bo22b2o3b2o5b2o3b2o$93bo8b2o22b2o3b
2o8bo$92b3o7bobo33bo5bo$91b5o43b2ob2o$90bobobobo43bobo$90b2o3b2o44bo$
127b2o12bo$126b2o$93bo31bo2bo2b2o$92bobo32bo3bo$91b2obo37b3o$91b3o40bo
$90bo2bo43bobo$90b3o44b2o$89bo3bo44bo3b3o$88bo5bo23bo22bo3bo$89bo3bo5b
o17b2o21bo5bo$90b3o7bo16bobo20b2obob2o$98b3o$131bo$129b2o$130b2o$111b
2o$110bobo32b2o$107bo4bo12b2o18bo$88b2o15bobo17b2o19b3o$89bo16b2o40bo$
86b3o26b2o21b2o$86bo29bo21bo2bo$92b2o22bobo9bo3b3o7bo$90bo3bo5bo2b3o
11b2o8b5o3bo6bo$89bo5bo9bo3bo16b2ob2o3bo7bo$88bo2bo3bo8bo4bobo13b3ob2o
3bo3bo2bo5b2o$95bo16b2o12b2ob4o5b2o7bobo$86bo3bo3bo17b2o13b4o18bo$85bo
b2o3b2o18b2o14bo20b2o$85bo23bobo4b2o$84b2o23bo6bobo$118bo$118b2o4$14b
2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o$12b2ob2o2b2ob2o2b2ob2o2b2ob2o2b
2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o$12b4o3b4o3b4o3b4o3b4o3b4o3b4o
3b4o3b4o3b4o$13b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o!

Notice that in the regular stream of LWSSes (the one in the bottom of this pattern) each LWSS takes up 7 cells (if we tried to squeeze them any more they'd destroy each other). We can now imagine using an LWSS stream to transfer information by making each 7 cells in the stream represent either a 1 or a 0 depending on whether those 7 cells contain an LWSS or not. Therefore in the regular LWSS stream the amount of bits per cell of the stream is 1b/7c ("1 bit per 7 cells").

Notice now, though, that for a stream of LWSSes to successfully pass through the Stargate the distance between consecutive LWSSes in the stream has to be increased, so in an LWSS stream which is to pass through the Stargate each LWSS doesn't take up 7 cells any more, but instead it takes up 30 cells. If we were to use this stream to transfer information analogously to the way we used a regular stream of LWSSes, the amount of bits per cell of this stream would therefore be reduced to 1b/30c.

Of course, it's not all about how spread out the bits in a stream are, it's also how fast they travel that's important, so now comes the calculation part. Instead of writing the speed of a spaceship the common way as, for example, "c/2", I'll write "1c/2g" instead, which stands for "1 cell per 2 generations", so it's the same thing, but this format better suits the calculations I want to do or, to be more precise, the value I want to get from those calculations.

Since the regular LWSS stream travels at 1c/2g and has information density of 1b/7c, the amount of bits per generation that a regular LWSS stream delivers is (1c/2g)*(1b/7c) = 1b/14g (1 bit per 14 generations).

Whether LWSS stream itself passes through the Stargate or not is, like I said, a philosophical question, but it is indisputable that the information which that stream carries does pass through the Stargate - if we interpret the LWSS stream that comes out of the Stargate the same way we would have interpreted the one that went in it we'll get the same stream of bits, so information does pass through the Stargate at the speed of 15c/14g, therefore the amount of bits per generation that an LWSS stream travelling through the Stargate delivers is (15c/14g)*(1b/30c) = 1b/28g.

Would you ever have guessed it - the amount of bits per generation that a regular LWSS stream can deliver is precisely two times greater than the amount of bits per generation that an LWSS stream travelling through a Stargate can deliver.

Of course, the immediately obvious remark to my calculation is that for the compact stream of LWSSes which transfers 1 bit of information per 14 generations to work one would need a device which is capable of reading the input LWSS stream at c/14. As a noob I'm not really familiar with which kinds of LWSS-stream-reading devices there are in Life, but checking out the Turing Machine (http://www.conwaylife.com/wiki/index.php?title=Turing_machine) it seems that what we have at the moment is this (the thing on the left in the pattern):

x = 150, y = 45, rule = B3/S23
114b2o$115bo$115bobo6bobo21b2o$116b2o5bo2bo21bo$122b2o10bo6bo4bobo$
120b2o3bo8bo5bobo3b2o$122b2o9bo6b2obo$123bo2bo2b2o9b2ob2o$124bobo2bo2b
3o5b2obo$129b4o7bobo6bo$130b2o9bo5b3o$32b2o28b2o28b2o28b2o22bo$31b4o
11b2o13b4o11b2o13b4o11b2o13b4o21b2o$30b2ob2o10b2ob2o10b2ob2o10b2ob2o
10b2ob2o10b2ob2o10b2ob2o$31b2o13b4o11b2o13b4o11b2o13b4o11b2o$47b2o28b
2o28b2o$143b3o$133b3o$22b2o109bo9bobo$20bo3bo109bo7b5o$11bo7bo5bo115b
2o3b2o$11bobo4b2obo3bo97b3o15b2o3b2o$14b2o3bo5bo99bo$14b2o4bo3bo7b2o
80bo9bo$14b2o6b2o8bobo78bobo25b2o$2b2o7bobo20bo78b2obo8bobo11b2obo$bob
o7bo22b2o77b2ob2o6bo2bo11bo$bo111b2obo6b2o$2o101b2o8bobo5b2o3bo13b3obo
$102bobo9bo8b2o19bo$102bo21bo2bo5b2o9bo$101b2o22bobo5bobo$135bo$135b2o
2$139b2o3b2o$141b3o$140bo3bo$141bobo$142bo2$139b2o$140bo$137b3o$137bo!

which is if I recognise it correctly a slight variation of Gosper glider gun, which can therefore obviously only read the input LWSS stream at c/30, meaning that each LWSS in the stream must take up 30 cells (which they indeed do there), which in turn means that the amount of bits per generation which can be received is (1c/2g)*(1b/30c) = 1b/60g. Yes, that's more than two times worse than what an LWSS stream travelling through the Stargate can do, but if we ever found a way to read the input LWSS stream sufficiently fast, the Stargate would obviously become completely useless.

Incidentally, the frequencies at which a regular LWSS stream is more than or equally efficient as a "Stargate LWSS stream" are pretty easy to calculate (I hope everyone can read Unicode, if not those weird symbols are the symbols for "greater or equal" in the first two lines and "less or equal" in the third line):

(1c/2g)*(1b/xc) ≥ (15c/14g)*(1b/30c)
(1/2)*(1/x) ≥ (15/14)*(1/30)
x ≤ 14

So if we ever found a device which is capable of reading the input stream of LWSSes at c/14 or faster, Stargate would become completely useless. But then again, I'm not entirely sure that we've got a device which can read it at c/30 (the frequency of Stargate-aided LWSS stream) in the first place...
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Re: Spaceship speed limits

Postby Phantom Hoover » May 20th, 2010, 12:03 pm

Allow me to clarify this to you. Information cannot travel more than 1cell/generation in Life. It is incredibly obvious; it derives from the axioms of Life. This is not a "philosophical" matter; it is hard mathematical reality. The Stargate does not send information at 15c/14; this is an illusion that derives from your godlike, three-dimensional observer status, able to instantly see the state of every cell in the universe.
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Re: Spaceship speed limits

Postby calcyman » May 20th, 2010, 12:18 pm

Doccolinni:

I believe that you have confused your 'p's and 'c's. 'c' is the fundamental unit for speed in Life; p is an abbreviation for period. For example, the Gosper glider gun is period-30, or p30. The period of a pattern is measured in generations per cycle, and is inversely proportional to frequency.

... 1b/14g (1 bit per 14 generations).


Your compound unit "b/g" is inversely proportional to the commonly accepted "p". So, "1b/14g" is equivalent to p14.



one would need a device which is capable of reading the input LWSS stream at c/14.


You mean period-14 -- c/14 is a measure of speed, not transmission rate. And yes, it is possible to read a LWSS stream at period-14:

x = 404, y = 460, rule = B3/S23
oo$bo$bobo$bboo4bobbo24bobbo10bobbo24bobbo10bobbo24bobbo$7bo6b4o10b4o
3bo6b4o3bo20b4o3bo6b4o3bo6b4o10b4o3bo$7bo3bobbo3bo9bo3bobbo3bobbo3bobb
o3bo16bo3bobbo3bobbo3bobbo3bobbo3bo9bo3bobbo3bo$7b4o3bo13bo6b4o3bo6b4o
17bo6b4o3bo6b4o3bo13bo6b4o$15bobbo10bobbo10bobbo24bobbo10bobbo10bobbo
10bobbo3$5bo$4boo$4bobo$$8boo$7boo$9bo$12bo$11boo$11bobo$$15boo$14boo$
16bo$19bo$18boo$18bobo$$22boo$21boo$23bo$26bo$25boo$25bobo$$29boo$28b
oo$30bo$33bo$32boo$32bobo$$36boo$35boo$37bo$40bo$39boo$39bobo$$43boo$
42boo$44bo$47bo$46boo$46bobo$$50boo$49boo$51bo$54bo$53boo$53bobo$$57b
oo$56boo$58bo$61bo$60boo$60bobo$$64boo$63boo$65bo$68bo$67boo$67bobo
184boo3booboo74boo3booboo$239bo14bobo3bobobo58bo14bobo3bobobo$71boo
166b3o10boobb4obbobo3bo54b3o10boobb4obbobo3bo$70boo170bo8bobboo3bobobo
3bobo56bo8bobboo3bobobo3bobo$72bo168boo8bobobbo4bo5bobo55boo8bobobbo4b
o5bobo$75bo174boob4o3boo4boobobo62boob4o3boo4boobobo$74boo168bo7bo3bob
oobobbo4boobo55bo7bo3boboobobbo4boobo$74bobo166bobo5boo3bobboo3bob3o3b
o54bobo5boo3bobboo3bob3o3bo$239boobboo7bo3boboobobbo5b3obo48boobboo7bo
3boboobobbo5b3obo$78boo159boo9boob4o3boo4boobo3bobo47boo9boob4o3boo4b
oobo3bobo$77boo172bobobbo4bo5boboboobbo59bobobbo4bo5boboboobbo$79bo
171bobboo3boboboboboboobobo60bobboo3boboboboboboobobo$82bo169boobb4obb
oboobboboboboo17booboo38boobb4obboboobboboboboo$81boo171bobo3bobo3bobo
bobobbo16bobboo5boo34bobo3bobo3bobobobobbo$81bobo170boo3boobobooboboo
bbo19bo4bobbobbo33boo3boobobooboboobbo$263bo3boboboo17b3ob4obobbobo42b
o3boboboo$85boo177bobobbobo17bobbobo4booboboo15bo26bobobbobo$84boo165b
o11booboobobobo16bobo3boo6bobbo13boo24booboobobobo$86bo165bo10bo5boobo
bo12b4obobo3boboobboboo12bobo24bo5boobobo$89bo160b3o12boobo5bo11bo4bo
4boo3boboobo42boobo5bo$88boo143boo31bob6o13b3o3b3obboobo4bo43bob6o$88b
obo143boo30bo4bo17bobobo3bobboob3o33bo10bo4bo$233bo33b3o20b3obboobo4bo
33bobo11b3o$92boo175boo14boo9boboboo36boo13boo$91boo191bobbo7bo3boboo$
93bo62boo126b3o9b3o$96bo58bobbo128b3o3b3o$95boo55bo3bobo125boo3bo3bo3b
oo$95bobo52b6obo126boboobb3obboobo$149bo5bo130bo4bo4bo$99boo48boboobo
bbo128bobbobobobbo$98boo50bo3boboo127boobo5boboo$100bo51bobo129bobbob
5obobbo41boo$103bo47boo3boo126booboboboboboboo34boo5boo$102boo46bobboo
bo129bobo5bobo6boo28boo$102bobo43bobbo3bobbo110bo16bo3b3o3bo7boo63boo$
148boobo3boboo9bo98bobo17b3obob3o7bo65bo$106boo41boboboobo9b3o47bo51b
oo19bobobo41boo33bo$105boo41bobb3obbo8bo50boo117boo19bo12boo$107bo40bo
bo3boboo7boo22boo24bobo60boo5boo3b3o36boo26bo$110bo38bob4obbo32bo87boo
5bo43boo24b3o$109boo40bo3bo7bo26bobo90bobo104booboo$109bobo39boboobbo
bboboboo25boobboo37bo48boo6bo92boo5boobbo$152boboboo9boo26boo35b3o44b
oo9bobo44boo14bo29bobbobbo4bo$113boo39bobo3bo7bo43boobbobo12bo47bobo9b
oo58boo14bo15bobobbob4ob3o$112boo39bobbo9boo43b3obo3bo11boo14boo31bo6b
oo61boo14boo14boobb3o4bobobbo$114bo39boo5bobboo44boo6bo28boo37bobo60bo
30bobbobo3b4obbobo$117bo44b3o46bob5o68bo5boo56b5o25boobob5obb3obb4o$
116boo29boo5boo56b4o37bo31boo5boo57bo29boboo5boo4bo4bo$116bobo29bo5boo
58bo35bo3bo126bo4boboobb3obob3o$148bobo95bo7bo23b5o99b3oboobbo3bobobo$
120boo27boo84bo9bobo3bobo22b3obob3o18boo39booboo35bo4boboo$119boo32boo
78b3o10b5o16bo7bo4bo4bo17bobo37bobobobo22boo12boobobo3b3o3boo$121bo30b
obo78b3o11b3o15boo8bobooboboobo17bo22boo16bobbobo21boo12boobo3bo7bobbo
$124bo28bo35boo41bo3bo6boo3b3o15boo5boobobo3boboboo39bo8b3o8boboo8bo
13bo15b3o9b3o$123boo63bobo16boo24b4o6boo5boo21bobbo7bobbo39bobo8bo7boo
3bo8boo30b4ob4o$123bobo62bo6b3o9bobo10bo12boobo13boobboo18boob7oboo41b
oo7b3o3bobobbobo8boo28boo3bobobo3boo$187boo6boobo10bo9bobo32boo19bo9bo
57boobbooboo37boboobb3obboobo$127boo9boo7boo44boobobo4boo4boo10boo52bo
9bo105bo3bobo3bo$126boo9bobboboobobbobbooboo47bobo24boo3bo37boboo7boob
o103bo9bo$128bo8bobo3boboobb3obob3o38boo7bo24bo3bobo36boo5bo5boo102boo
b7oboo$131bo6boboo5boo4bo4bo46boo10boo12bo3boo39b9o104bobbobo3bobobbo$
130boo8bobooboobboboob4o22boo34bobo13bo40b3obbo3bobb3o101boobobo3bobob
oo$130bobo7bobo3bobbobbobo12bobo9boo35bo13bob5o32boobo3bobbobobbobbo
103boboo3boobo$139boobb3obo4bobbo12boo11bo33boo13boo4bo33boobobo9boo
104bo3b3o3bo$134boo4bobobbob4ob3o13bo64b3o32bo4boboo115b3obob3o$133boo
5bobbobbo4bo78boobo32b3oboobbo3booboo14boo95bo3bo$135bo5boo5boobbo77bo
bo32bo4boboobb3o3b3o11bobbo$126boo10bo8booboo88b3o22boboo5boo4bo4bo7bo
3bobo29boo$125bobbo8boo100bobbo21boobob3obobboboob4o6b6obo21b3o6bo15b
oo43bo$125bobo3bo5bobo103bo4bobo13bobbo5bobboobobo8bo5bo23bo9bo14bo43b
oo$126bob6o105boo7boo16booboboo4bobobbo7boboobobbo22bo24b3o40bobo4bo$
128bo5bo6boo96boo3bo4bo17bobobbob4ob3o9bo3boboo29bo19bo27bobo16bobo$
126bobboboobo5boo91bo10bo22bobbobbo4bo14bobo35bo45boo16boo$126boobo3bo
8bo89bo9bo25boo5boobbo12boo3boo29bobbo45bo21boo$129bobo13bo86b3o5b3o
31booboo12bobboobo32b3o66bobo$126boo3boo11boo49bo11bo32boo47bobbo3bobb
o30b3o61boo5bo$127boboobbo10bobo12boo36bo7b3o32bo48boobo3boboo9bo19bo
bbo9bo51boo5boo$115bo9bobbo3bobbo23bo37bo6bo38bo46boboboobo9b3o19bobo
8b3o$102booboo8b3o7boobo3boboo12boo6boobo38boo4boo33b6o44bobb3obbo8bo
22b3o7bo$96boo5boobbo10bo8boboobobo12boo7bobb4o22bo11bobo38b5o46bobo3b
oboo7boo31boo52bo$95bobbobbo4bo10boo8bobb3obbo13bo7boo3boo22boo10b3o
37bo3bo47bob4obbo93bobo$95bobobbob4ob3o16boobo3bobo16bo6boo24boo13bo
38b3obo48bo3bo7bo75boo10bobo$94boob4o4bobobbo9bo5bobb4obo16boo6bobboo
34boo39bob3o48boboobbobboboboo73boobboo5boobobo$95bobo4boo3bobobbo6bob
o6bo3bo18bobo7boo35boo43bo49boboboo9boo74bobo3bo3boobo$95bob4o4b3ob3ob
oboobboo5bobboobo14boo89b3o8boboo42bobo3bo7bo75bo4boobo3bo$93boboo5boo
4bo4boboo9boobobo14bobbo5boo92boobo41bobbo9boo81bo3b4obo$92bobo3boboo
bb3obob3o14bobo11bobbobbobo4boo18bobbo117boo5bobboo37boo36boo7boo5bobo
$92bobboboobobbobbo3bo16bobo11b5oboboo5bo16bo129b3o38bo38bo8boboboobbo
$93boo7boo24bo18boo3bo6bo13bo3bo54b3o53boo5boo45bobo35b3o9bo4bobo$108b
o34b3obboo8boo13b4o57bo54bo5boo45boo36bo9booboboboboo$108bo33bobobbobo
3bo4bobo54bo17bo55bobo98bobbobobobbo$110b3o29boboobboo49boo14bobo72boo
100bobo3bo$109b5o29bo3boo3bo9boo35boo14boo77boo32boo61boo3boo$108bobbo
boo29booboboo10boo130bobo31bobo64bobo$109b5o31bobobo13bo130bo32bo63b4o
3bo$105boo3boo32bobbobo47boo5boo34boo84boo63bo4boobo$104bobo5bo31boobb
o49bo5boo32b3o95b3o54bo5bo$104bo5boo19bo66bobo36bo4bo93boobo51bob6o$
103boo5boo17bobo67boo36bob6o34boo7boo44boobobo4boobo42bobo3bo$130boo
37boo32boo31boobo5bo32bobboboobobbobbooboo47boboo42bobbo$168boo32bobo
29bo5boboobo32bobo3boboobb3obob3o38boo27boo23boo$170bo32bo30booboobo3b
o34boboo5boo4bo4bo65bobbo$173bo61bobobbobo38bobooboobboboob4o22boo42bo
bo3bo$156bo15boo60bo3bo3boo37bobo3bobbobbobo12bobo9boo44bob6o$155b3o
14bobo26b3o21boo3boobobooboboobbo35boobb3obo4bobbo12boo11bo45bo5bo$
154boobo29boo7boo17boo8bobo3bobo3bobo3bobbo34bobobbob4ob3o13bo56bobbo
bbobo$154b3o19boo8bobboboobobbobbobobo7bo3bo6boobb4obboboobbo3boboo34b
obbobbo4bo73b4obobo$155boo18boo9bobo3boboobb3obob3o4bo4bo5bobboo3bobob
oboboboobobo36boo5boobbo75bobo$177bo9boboo5boo4bo4bo6bo7bobobbo4bo5bo
bb3obbo41booboo73boo3boo$180bo8bob5obb3obb4o3bobbo7booboobo4boo3boobo
3bobo120boboobbo$129b3o47boo8bobo3b4obbobo6boo9bo5bo4bobobbobb4obo109b
o9bobbobobobbo$129bo49bobo6boobb3o4bobobbo9b3o4b4obbo3boo6bo3bo111b3o
7boobo3boboo$130bo58bobobbob4ob3o10boo5bo5bo4bobobbobboobo114bo8boboob
obo$189bobbobbo4bo12boo6booboobo4boo3boobobo114boo8bo3boobbo$148bo41b
oo4b3obbo10boo8bobobbo4bo5bobo125boobo3bobo$149bo48b4o11bo8bobboo3bobo
bo3bobo119bo4bobb5obo$147b3o25boobobo6bo22b3o10boobb4obbobo3bo96bo11bo
10bobobb3obo3bo$124bo49bobb3obo4boo12boo8bo14bobo3bobobo102bo7b3o6boo
bboo4bo3boobo$122b3o48bobo5bo4bobo11bo24boo3booboo103bo6bo9boo9boobobo
$106bo14bo52bob6obo13boobo138boo4boo20bobo$106b3o12boo53bo5bobo5boo5bo
bb4o122bo11bobo26bobo$109bo64bobbobbobobo4boo7boo3boo122boo10b3o26bo$
108boo8boo54b4obobobboo5bo8boo124boo13bo$124bobo50bobo4bo9bo5bobboo
134boo$124bo18boo29boo3boo5bo6boo7boo135boo24bo$109boo64boboobbo3boobb
o3bobo167bobo$109boo12boo3bo14bobo27bobbobobobbobbobobo173boo$123boobo
bo18bo15bo9boobo3boboobobbobo6boo46bobbo66bobbo$125bo19booboboo11b3o9b
oboobobobbooboboo4boo11b4o31bo34b4o31bo$147boobo8boo5bo8bo3boo3bo3boo
3bo4bo10bo3bo30bo3bo30bo3bo30bo3bo$149bo9boo4boo7boobo3b3oboobboo18bo
34b4o31bo34b4o$173bobb5obbobobbobo3bo15bobbo66bobbo63bo$168bo3b3obo4bo
bb3obboo149boo5boo$125boo40bobo3bo3b4o7boo3bo146boo4bobo$125bo19boo16b
oobboo5boobo3b6oboboo$126b3o15bobo16boo10bobobobbobbobbobo80boo$128bo
15bo30boboboo6bobbo77bo3bo$122boo19boo31bo11boo18bo57b6o3boo$122bo84b
oo56bo5bobobbo$123b3o71bo9bobo55bobobbobb3o$125bo51boo5boo10b3o67bobob
3o$112b3o61bobo5bo11boboo11boo55bobobbo108bo$112bobbo59b3o4bobo12b3o
10boo55boo3boo109bo$111bo3bo58b3o5boo13boo13bo53bobboobo108b3o$112bobb
oo57boo3boo34bo48bobbobobobbo$105bo8bo16bo26boo13boo4boo33boo48boobo3b
oboo9bo$105bobo4boo15b3o27boo13boo38bobo48boboboobo9b3o$105boo4b3o14bo
29bo19bo85bobboo3bo8bo$111b3o14boo134bobo3boboo7boo22boo87boo5boo$124b
oo139bob5obbo31bo22boo63boo5bo$123bo143bo3bob3o3bo26bobo21boo67bobo$
124bobo50booboo85boboo3bo3bobo26boobboo16bo20bo48boo$125bo49b3obob3o
84boboboo5boobboo26boo35b3o44boo$174bo4bo4bo85bobo10boo62bo47bobo$174b
obooboboobo84bobbo59boo13boo14boo31bo$172booboboobooboboo38boo43boo59b
oo30boo$172bobbo3bo3bobbo37boo55boo49boo62bo$173boob7oboo40bo36boo5boo
8boo51b3o60bo$174bo9bo44bo34bo5boo10bo26bobo23bo33boo$174bo3bobo3bo43b
oo34bobo41bobbo23b4o25bo4boo13bobo7bo3bo$126boobbooboo37boboobo3boboob
o41bobo34boo41bo3bo24boo24b3o18boo6b3o3b3o$111boo13bobobbobo38boo11boo
82boo37bobo25b3o16boo5b3obo18bo5bo3b3o3bo$88bo21bobo8bo7boo3bo6bo14bob
o16b9o48boo34bobo41boo21bobo15boobbo33boboo3boobo$87bo22bo9bobo7boboo
7boo13boo14b3obbo3bobb3o44boo36bo35bo7bo21bo3bobbo10bobb3o30boobobobob
oboboo$87b3o19boo8booboo3bobbobo7bobo14bo10boobo3bo3bo3bobbo46bo70bob
oobobbo10boo11b6o11bo4bo30bobbobobobobobbo$119bobbo3bobobobo36boobobo
4bo4boo118bo5b3o10bobo9boobboo13b5o5b3o3boo18boobo5boboo$118bo3bo4boob
oo35bo4boboo92b3o32boo20bo30boo4b5o3boo19bo3bobo3bo$122bo42b3oboobbo3b
o3bo72boo7boo54boo4boo8bo26booboo24bo9bo$147boo15bo4boboobb3obob3o69bo
bboboobobbobbobobo47bobo14b3o7boo3bo12bo24boboobb3obboobo$68boo5boo60b
oobbobo3bobob3o10boboo5boo4bo4bo68bobo3boboobb3obob3o7bo39bo14b3o7bo3b
obo36boo3bobobo3boo$69bo5boo59b3obo3bobbobo13boobob4o4b3ob4o70boboo5b
oo4bo4bo7boo28boo7boo10boo12bo3boo39b3o3b3o$69bobo63boo6bo3b3o13bobbob
o4boo3bobo75bob5obb3obb4o7boo29boo18bobo13bo40b3o9b3o$70boo64bob5o3bo
3bo14boob4o4bobobbo61bo12bobo3b4obbobo61bo13bob5o11boo19boobo3bo7bobbo
$74boo46bo14b4o4bo4bo15bobobbob4ob3o61boo11boobb3o4bobobbo27bo31boo13b
oo4bo11boo20boobobo4bo4boo$73bobo45boo16bo6bo3bo15bobbobbo4bo19bo44bob
o11bobobbob4ob3o27boo49b3o32bo4boboobb3o$74bo43bo28bo19boo5boobbo17b3o
57bobbobbo4bo30bobo45boobo32b3oboobbo3bobobo$117bobo53booboo17boobo47b
oo9boo5boobbo77bobo19bo12bo4boboobb3o3b3o$74bo37boo3bobbo6boo66b3o47b
oo16booboo98boo13boboobo3boo3boo4bo$74bo37boo6bo16boo57boo49bo119boo
11boobob3obobboboob4o$117bobbo15bobo13boo96bo129bobbo5boobobbobo$72bo
3bo7bobo29bobbobboo14bo14bo95boo100bo30boobb3o4bobobbo$70b3o3b3o6boo
30boo3boo28bo96bobo99bobo29bobobbob4ob3o$69bo3b3o3bo5bo30boo34boo197b
oo3b3o24bobbobbo4bo$69boboo3boobo36boo238bobbo24boo5boobbo$67boobobobo
boboboo34boo5boo229bo4bo30booboo$67bobbobobobobobbo41boo187bo10bo$68b
oobo5boboo188boo39b4o7b3o29bo5bo$69bo3bobo3bo189bo28bobo9b4o6bo$69bo9b
o186boobo29boo19boo32boo4bo$67boboobb3obboobo184bobboobo26bo56boo3bo$
67boo3bobobo3boo178boo5boo3bo37b4o43bo3bo$70b3o3b3o180boo8boobo37b3o
47bo$67b3o9b3o179bo7bobo39bo42boo3boo$67bobbo7bo3boboo178bo8bo80b3o$
68boo4bo4boboboo51boo119boo4boo7bo82bo9boboo$73b3obboobo4bo47b3o119bo
bbo3bobo99boobo$72bobobo3bobboob3o30b3o11bo4bo112bobbobbobo$70b3o3b3o
bboobo4bo12bo18bo11bob6o110b5oboboo6boo25b4o36bo$69bo4boo3boo3boboobo
13boo15bo11boobo5bo115bo3bo4boo26bo3bo34bo$70b4oboobobbob3oboboo11boo
26bo5b4obo111boobo4bo6bo25bo38b3o$73bobobboboo5bobbo39booboobobobo111b
o3boo3bo33bobbo47boo$72bobbobo4b3obboo42bobobbobo113bobobo4bo53boo28bo
bo22boo$73b3ob4obobbobo42bo3boboboo113bo3bo3bo53boo30bo21bobbo$76bo4bo
bbobbo33boo3booboboobo5bo113booboboo108bobo3bo$75bobboo5boo34bobo3bobo
3bobobobobbo112bobobo110bob6o$76booboo38boobb4obboboobboboboboo93boo
16bobbobo53boo5boo50bo5bo$118bobboo3bobobobobo4bobo93bobbo15boobbo55bo
5boo48bo4boobo$118bobobbo4bo5boboboobbo92bobo3bo36bo35bobo53b4o3bo$
106boo9booboobobboboo3boobo3bobo24boo67bob6o33boo36boo56bobo$106boobb
oo5bo3bobobobbo7b4obo24bobbo27bo40bo5bo32bobo39boo49boo3boo$110bobo5b
3oboo4boboobboo3bo26bobo3bo23b3o37bobb4obo73bobo50bobo3bo$111bo5bo3bob
obobbo7boobo27bob6o21boboo36boobobobo75bo39bo9bobbobobobbo$117booboobo
bboboo3boobobo30bo5bo21b3o39bobo117b3o7booboboboboo$108boo8bobobbo4bo
5bobo30bobboboobo21boo37booboboo119bo8bo4bobo$91booboo3boo8bo8bobboo3b
obobo3bobo30boobo3bo62bo5bo41bo75boo8boboboobbo$90bobobo3bobo5b3o6bo3b
oobb4obbobo3bo34bobo52bo9bobbobobobbo38boo17boo7boo14bobo39boo5bobo$
86bo3bobobb4obboo3bo6b3o5bobo3bobobo35boo3boo38booboo8b3o7booboboboboo
38bobo15bobboboobobbobb5o8boo8bo24bo4bo3b4obo$85bobo3bobobo3boobbo8bo
8boo3booboo37boboobbo31boo5boobbo10bo8bo4bobo57bobo3boboobb3obob3o6bo
8bobo22bobo3boobo3bo$85bobo5bo3boobbobo8boo42bo9bobbo3bobbo28bobbobbo
4bo10boo8boboboobbo57boboobo3boo4bo4bo14bobo18boobboo4bo3boobo$83bobob
oo4boo5booboo38booboo8b3o7boobo3boboo28bobobbob4ob3o16boobo3bobo59bob
ooboobb4ob4o3boo9boobobo16boo9boobobo$82boboobbo7bo3bobobbo4bo26boo5b
oobbo10bo8boboobobo28boobb3o4bobobbo9bo8b4obo60bobo4boobobobo6boobboo
8boobo27bobo$82bo3b3o7bo3boobb3obbobo24bobbobbo4bo10boo8bobb3obbo28bob
o3b4obbobobbo6boboboobboo3bo61boob4obobbobobbo9boboboobboo3bo27bobo$
80bob4obbo7bo3bobobbo4boobboo20bobobbob4ob3o16boobo3bobo28bob5obb3obb
3oboboobboo8boobo62bobobbob4ob3o11bo8b4obo15boo9bo$79bobo3boboo4boo5b
ooboo9boo19boob4o4bobobbo9bo5bobb4obo27boboo5boo4bo4boboo9boobobo63bo
bbobbo4bo20boobo3bobo13bobo$79bobb4obo5bo3boobbobo32bobo4boo3bobobbo6b
obo6bo3bo29boo3boboobb3obob3o14bobo26bo39boo5boobbo10boo8boboboobbo15b
o$80bobobbobobobobobo3boobbo32bob4o4b3ob3oboboobboo5bobboobo32booboobb
obbobobo16bobo25b3o27boo15booboo12bo8bo4bobo$79boobobobobboobobb4obboo
31boboo5boo4bo4boboo9boobobo34bo4boo18bo5bo26boboo25boo30b3o7boobobobo
boo$79bobb3obobo3bobo3bobo32bobo3boboobb3obob3o14bobo34bobo9b3o10bobo
33b3o27bo29bo9bobbobobobbo$81bo3bobobooboboo3boo32bobboboobobbobbo3bo
16bobo34boo24boo33boo70bo5bo$82boobobo3bo42boo7boo24bo167booboboo$83bo
4bobo58bo69bo120bobo$81bobob4oboo57bo68bobo116boobobobo$80bob4o5bo10bo
48b3o65boo81boo33bobb4obo$80bo5boboo11bo17boo29b5o60boo84boo36bo5bo$
81b6obo12b3o14boo29bobboboo58bobo86bo33bob6o$83bo4bo31bo29b5o59bo5boo
114bobo3bo35bo$85b3o58boo3boo60boo5boo114bobbo39boo$84boo59bobo5bo183b
oo39boo6boo5boo$145bo5boo19bo213boo5bo$144boo5boo17bobo58boo158bobo$
171boo58bobo109b3o45boo$231bo113bo41boo$313bo30bo42bobo$249bo62boo74bo
$197bo52bo61bobo$196b3o49b3o149boo$195boobo189bo10bobo$195b3o189b3o3b
oo4bo$196boo188bobobobbobbooboo$320bo63b3o3b3obboobo3boo$84bo52bo181b
oo62bo4boo3boo3boboobo$84bobo49boo32b3o146bobo62b4oboobobbob3obo$84boo
50bobo31bo138boo61bo14bobobboboo5bo$68boo5boo94bo138bo60bo14bobbobo4b
3obboo$69bo5boo233bobo58b3o13b3ob4obobbobo$69bobo117bo44bo76boo77bo4bo
bbobbo$70boo48bo42bo26bo41b3o81bo72bobboo5boo$74boo44b3o38b3o24b3o25bo
14bo16b3o64bobo8boo62booboo$73bobo47bo16boo18bo55b3o12boo15bo65boobo7b
obo$74bo31boo14boo11boobb3obboo14boo57bo24bo4bo16bo47bobo10bo$106boo
27bobbobo4boo71boo17boo3bo3bo18b3o46bobo$74bo61bo3boboobo90b3o3bo21boo
bo44bobboo$74bo64bo3boo92bo3bo5boo15b3o49bo$100boo117boo19boo6bo16boo
48bo$72bo3bo23boo63bobo51boo27bo66bo$70b3o3b3o25boo59bo18boo52bo5boboo
64bobo$69bo3b3o3bo24boo12bobo117boobbo71bo$69boboo3boobo8bo21bo7bobobo
41boo3bo14bobo53boo27boo55boo9boo$67booboboboboboboo7boo18bobo11boo39b
oobobo18bo80boo35boo5b3o10bo9boo$67bobbobobobobobbo6boo32bo23boo18bo
19booboboo34bo77bobo16bobo11bo$68boobo5boboo18boo44bobo40boobo8boo24b
3o76bo18boo28bo$69bo3bobo3bo19boo44bo44bo9boo23boobbo5boo67boo48bobo$
69bo9bo52boo10boo10boo71bo5bo19boo97boo$67boboobb3obboobo37bo3boo32bo
52booboobboo9bo7b3o15bobo52boboo$67boo3bobobo3boo36bobo3bo29b3o9boo43b
obobbobo5bo13bo15bo52b3oboo$70b3o3b3o39boo3bo12boo16bo11bo19boo22bo3b
oo8bobo5boo19boo51bo$67b3o9b3o40bo13bobo28bo17bobo23boobo9boo6bo74b3ob
oo$67bobbo7bo3boboo32b5obo13bo27boo17bo26bobobbo15b3o73bobo6b3o18bo$
68boo4bo4boboboo33bo4boo13boo44boo25bobbobobo16bo73bobo6bobbo16bobo$
73b3obboobo4bo32b3o70bo9boo5bobb3oboo92bo6bobboo16bobo$72bobobo3bobboo
b3o23b3o6boboo66bobo7b4o4b3o19boo84boo17boboboo9boo$70b3o3b3obboobo4bo
22bobo7bobo67bo7bo4bo6bo17b4o101boboo3bo4boobboo$69bo4boo3boo3boboobo
21bobbo84boo4boo4boo16bo4bo21boo55boo6bo13bo3bob3obbobo$70b4oboobobbob
3oboboo20b3o76b5o4boo4boo21boo4boo19bobbo53bobo7boo9bob5obbo4bo$73bobo
bboboo5bobbo20b3o71boobbo4bo5bo4bo22boo4boo19bobo3bo50bo8boo9bobo3bob
oo$72bobbobo4b3obboo16bobo4bobbo69bobbobbo9b4o24bo4bo21bob6o47boo19bo
bboo3bo8boo$73b3ob4obobbobo18boo4bo73boboboo10boo9boo15b4o24bo5bo68bob
oboobo8bo$76bo4bobbobbo18bo8bo69boobo5bo16b3oboo14boo23bobboboobo67boo
bo3boboo7b3o23boo$75bobboo5boo35bo65bo4bobo15boboboo39boobo3bo68bobbob
obobbo9bo22bobbo$76booboo42bo64boobbobbo13boobo46bobo72bobboobo34bobo
3bo$121b3o69boo61boo3boo66boo4boo3boo34bob6o$208bo16boo30boboobbo41bo
23bobo4bobo39bo5bo$110boo112bobbobboo23bobbo3bobbo39b3o23bobbobob4o34b
obbobbobo$224bobo4bobbo10bo9boobo3boboo42bo22bobobobbobbo34b4obobo$
225bo5bobobo9b3o9boboobobo42boo14boo5boobo5bo39bobo$228boobobbo13bo8bo
bb3obbo57boo9b6obo34boo3boo$111bobo94bo3boo14bobbo15boo7boobo3bobo70bo
3bobo34boboobbo$112bo94bobo3bo11bo4bo25bobb4obo74bobbo32bobbobobobbo$
111bo83bo11boo3bo12b5o20bo7bo3bo56bo20boo23bo9boobo3boboo$102boobo9bo
77b6o12bo37bobo4bobboobo55b3o44b3o9boboobobo$102boboo9bo77boobboo8b5ob
o13boobo14boobboo5boobobo55boobbo46bo8bo3boobbo$207bo4boo13boboo14boo
10bobo61boo44boo7boobo3bobo$119b3o75bo6booboboo46bobo58b3oboo51bobb5ob
o$119bo73boobbo6boboboboboo44bo60bobboo47bobb3obo3bo$120bo72boo3bo7bo
4bobo104b3o48bobo3bo3boobo$197bo8boo38boo73boo42boobboo5boobobo$140bo
54bobo49boo10boo5boo22boo29boo42boo10bobo$138bobo55bo49bo12boo5bo22bo
bbo31boo51bobo$139boo123bobo22bobo3bo28bobo44bo6bo$264boo24bob6o16bo
11bo45bo$149boo5boo102boo30bo5bo15bobo9boo42b3o$149boo5bo56bo46bobo27b
obb4obo15boo63boo5boo$154bobo54b3o47bo28boobobobo81boo5bo$154boo54bo
82bobo88bobo$150boo42boo14boo62boo14booboboo87boo$150bobo41boo65bo11bo
bbo14bo5bo82boo$151bo99bo8b3o3boo6b3obbo9bobbobobobbo33bo46bobo$181bo
67boo8bobobobbobbob3o5b3o7booboboboboo31b3o47bo$181bobo66boo5b3o3b3obb
oobo3boo5bo8bo4bobo31bo$137boo42boo73bo4boo3boo3boboobo4boo8boboboobbo
14boo14boo$137bobo17boo7boo89b4oboobobbob3obo15boobo3bobo14boo3bo$131b
o5bo12b5obbobboboobobbo91bobobboboo5bo9bo8b4obo19b3o65boo7boo$130bobo
15b3obob3obboobo3bobo60bo29bobbobo4b3obboo7boboboobboo3bo20booboo57boo
boobbobboboobobbo$130bobo14bo4bo4boo3boboobo31boo28boo28b4ob4obobbobo
4boobboo8boobo24bo31boo22b3obob3obboobo3bobo$128boboboo9boo3b4ob4obboo
boobo32bobo27bobo21booboo6bo4bobbobbo4boo9boobobo58boo20bo4bo4boo5boob
o$127boboo8boobboo6boboboboo4bobo31boo52bobboo5boobb3o4boo17bobo25bo
33bo23b4oboobobbooboobo$127bo3boobboobobo9bobbobobbob4oboo32bo8boobboo
boo35bo4bobbobboo26bobo3bo20boo45bobo12bobobbobbo3bobo$125bob4o8bo11b
3ob4obobbobo27boo4bobo6bobobbobo33b3ob4obobbobobboo24bo3bo21bobo44boo
12bobbo4bob3obboo$124bobo3boboo20bo4bobbobbo26bobo6boo8boo3bo31bobbobo
4b3obbo3bo12boo14b3o67bo13b3ob4obobbobo$124bobboobobo8boo10bobboo5boo
27bo7b3o9boboo33bobobboboo5bobo13bobo34bo66bo4bobbobbo$125bobo4bo8bo
12booboo32boo16bobbobo31b4oboobobbob3oboboo14bo34boo64bobboo5boo$124b
ooboboboboo7b3o63bobobobo30bo4boo3boo3boboobo51bo10boobbooboo46booboo$
124bobbobobobbo9bo64booboo32b3o3b3obboobo4bo47boo13bobobbobo$126bo5bo
115bobobo3bobboob3o47bobo16boo3bo$127booboboo30bo67bobo14b3obboobo4bo
49bo19boboo$128bobo19boo5boo4bo46boobboo16boo10boo4bo4boboboo50boo16bo
bbobo$126boboboboo17bo5boo4b3o48b3o16bo9bobbo7bo3boboo62bob3obobobo$
125bob4obbo17bobo55bo33b3o9b3o67b3obooboo$125bo5bo20boo62bobo6boo4boo
13b3o3b3o70bo$126b6obo22boo51bobbob4o6bobo4boo10boo3bobobo3boo39bo$
128bo3bobo20bobo52b3ob3o9bo16boboobb3obboobo40boo36bo16b3o$131bobbo21b
o88bo9bo41boo37boo14b4o$132boo111bo3bobo3bo79bobo13boobboo$194boo48boo
bo5boboo95boboo$194boo47bobbobobobobobbo21bo45b3o25b3o$141boo7boo48boo
32boo7booboboboboboboo21bobo42bobobobo23bo$140bobboboobobbobb5o41boo
33bo9boboo3boobo6b3o14boo43bo3boboo$140bobo3boboobb3obob3o73bo10bo3b3o
3bo8bo59boobbobo$141boboobo3boo4bo4bo72boo10b3o3b3o8bo50boo10bo5bo$
143bobooboobb4ob4o37boo48bo3bo61boo10bobboboo$143bobo4boobobobo40boo5b
oo113boo5boboo23boo$142boob4obobbobobbo46boo43bo69boo33bo$143bobobbob
4ob3o14bobo75bo103bo$143bobbobbo4bo18boo179boo$144boo5boobbo17bo76bo
67boo29boo$150booboo94bobo66boo5boo20b3o$207b3o40boo73boo5boo12bo4bo$
209bo36boo66bobo14bobo12bob6o$208bo36bobo67boo16bo11boobo5bo$245bo5boo
62bo27bo5bobbobo$218boo24boo5boo90boob4obobo$216b3o43bo81bobobbobo$
215bo4bo40bo81bo3bo3boo$215bob6o30bo7b3o70boo3boobobooboboobbo$214boob
o5bo28bobo79bobo3bobo3bobobobobbo$212bo5b4obo28bobo10boo65boobb4obbob
oobbo3boboo$212boob4obobo27boboboo5boobboo64bobboo3boboboboboboobobo$
213bobo4bo28boboobbo4bobo68bobobbo4bo5bo3boobbo$212bo3boboboo27bo3b3o
5bo57boo9boob3o4boo4boobo3bobo$190bo12boo3booboboobobo3bo24bob4obbo63b
oobboo7bo4bobo5bobb5obo$191boo10bobo3bobo3bobob3obbo21bobo3boboo7boo
58boboboo3boboo3boo3b3obo3bo$190boo9boobb4obboboobboboboboo21bobb4obo
8bo60bo7bo4bobo5bo3boobo$200bobboo3bobobobobobobbobo23bobobbobo9b3o63b
oob3o4boo4boobobo$200bobobboo3bo5bob4obbo21booboboboboo9bo54boo8bobobb
o4bo5bobo$188boo9booboo5boo4boobo3bobo21bobb3obobbo65bo8bobboo3bobobo
3bobo$188boobboo4bobbobo3bo7bobb4obo24bo3bobo64b3o10boobb4obbobo3bo$
192bobobb3obboo3bo7b3o3bo27booboboo63bo14bobo3bobobo$193bo4bobbobo3bo
7bobboobo28bo4bo78boo3booboo$199booboo5boo4boobobo27bobob3o$190boo8bob
obboo3bo5bobo28bob4obb3o$191bo8bobboo3bobobo3bobo28bo5bobobbo$188b3o
10boobb4obbobo3bo30b6o3boo$188bo14bobo3bobobo36bo3bo$203boo3booboo40b
oo!
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calcyman
 
Posts: 1147
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

Postby doccolinni » May 20th, 2010, 12:48 pm

calcyman wrote:Doccolinni:

I believe that you have confused your 'p's and 'c's. 'c' is the fundamental unit for speed in Life; p is an abbreviation for period. For example, the Gosper glider gun is period-30, or p30. The period of a pattern is measured in generations per cycle, and is inversely proportional to frequency.

... 1b/14g (1 bit per 14 generations).


Your compound unit "b/g" is inversely proportional to the commonly accepted "p". So, "1b/14g" is equivalent to p14.



one would need a device which is capable of reading the input LWSS stream at c/14.


You mean period-14 -- c/14 is a measure of speed, not transmission rate. And yes, it is possible to read a LWSS stream at period-14:

x = 404, y = 460, rule = B3/S23
oo$bo$bobo$bboo4bobbo24bobbo10bobbo24bobbo10bobbo24bobbo$7bo6b4o10b4o
3bo6b4o3bo20b4o3bo6b4o3bo6b4o10b4o3bo$7bo3bobbo3bo9bo3bobbo3bobbo3bobb
o3bo16bo3bobbo3bobbo3bobbo3bobbo3bo9bo3bobbo3bo$7b4o3bo13bo6b4o3bo6b4o
17bo6b4o3bo6b4o3bo13bo6b4o$15bobbo10bobbo10bobbo24bobbo10bobbo10bobbo
10bobbo3$5bo$4boo$4bobo$$8boo$7boo$9bo$12bo$11boo$11bobo$$15boo$14boo$
16bo$19bo$18boo$18bobo$$22boo$21boo$23bo$26bo$25boo$25bobo$$29boo$28b
oo$30bo$33bo$32boo$32bobo$$36boo$35boo$37bo$40bo$39boo$39bobo$$43boo$
42boo$44bo$47bo$46boo$46bobo$$50boo$49boo$51bo$54bo$53boo$53bobo$$57b
oo$56boo$58bo$61bo$60boo$60bobo$$64boo$63boo$65bo$68bo$67boo$67bobo
184boo3booboo74boo3booboo$239bo14bobo3bobobo58bo14bobo3bobobo$71boo
166b3o10boobb4obbobo3bo54b3o10boobb4obbobo3bo$70boo170bo8bobboo3bobobo
3bobo56bo8bobboo3bobobo3bobo$72bo168boo8bobobbo4bo5bobo55boo8bobobbo4b
o5bobo$75bo174boob4o3boo4boobobo62boob4o3boo4boobobo$74boo168bo7bo3bob
oobobbo4boobo55bo7bo3boboobobbo4boobo$74bobo166bobo5boo3bobboo3bob3o3b
o54bobo5boo3bobboo3bob3o3bo$239boobboo7bo3boboobobbo5b3obo48boobboo7bo
3boboobobbo5b3obo$78boo159boo9boob4o3boo4boobo3bobo47boo9boob4o3boo4b
oobo3bobo$77boo172bobobbo4bo5boboboobbo59bobobbo4bo5boboboobbo$79bo
171bobboo3boboboboboboobobo60bobboo3boboboboboboobobo$82bo169boobb4obb
oboobboboboboo17booboo38boobb4obboboobboboboboo$81boo171bobo3bobo3bobo
bobobbo16bobboo5boo34bobo3bobo3bobobobobbo$81bobo170boo3boobobooboboo
bbo19bo4bobbobbo33boo3boobobooboboobbo$263bo3boboboo17b3ob4obobbobo42b
o3boboboo$85boo177bobobbobo17bobbobo4booboboo15bo26bobobbobo$84boo165b
o11booboobobobo16bobo3boo6bobbo13boo24booboobobobo$86bo165bo10bo5boobo
bo12b4obobo3boboobboboo12bobo24bo5boobobo$89bo160b3o12boobo5bo11bo4bo
4boo3boboobo42boobo5bo$88boo143boo31bob6o13b3o3b3obboobo4bo43bob6o$88b
obo143boo30bo4bo17bobobo3bobboob3o33bo10bo4bo$233bo33b3o20b3obboobo4bo
33bobo11b3o$92boo175boo14boo9boboboo36boo13boo$91boo191bobbo7bo3boboo$
93bo62boo126b3o9b3o$96bo58bobbo128b3o3b3o$95boo55bo3bobo125boo3bo3bo3b
oo$95bobo52b6obo126boboobb3obboobo$149bo5bo130bo4bo4bo$99boo48boboobo
bbo128bobbobobobbo$98boo50bo3boboo127boobo5boboo$100bo51bobo129bobbob
5obobbo41boo$103bo47boo3boo126booboboboboboboo34boo5boo$102boo46bobboo
bo129bobo5bobo6boo28boo$102bobo43bobbo3bobbo110bo16bo3b3o3bo7boo63boo$
148boobo3boboo9bo98bobo17b3obob3o7bo65bo$106boo41boboboobo9b3o47bo51b
oo19bobobo41boo33bo$105boo41bobb3obbo8bo50boo117boo19bo12boo$107bo40bo
bo3boboo7boo22boo24bobo60boo5boo3b3o36boo26bo$110bo38bob4obbo32bo87boo
5bo43boo24b3o$109boo40bo3bo7bo26bobo90bobo104booboo$109bobo39boboobbo
bboboboo25boobboo37bo48boo6bo92boo5boobbo$152boboboo9boo26boo35b3o44b
oo9bobo44boo14bo29bobbobbo4bo$113boo39bobo3bo7bo43boobbobo12bo47bobo9b
oo58boo14bo15bobobbob4ob3o$112boo39bobbo9boo43b3obo3bo11boo14boo31bo6b
oo61boo14boo14boobb3o4bobobbo$114bo39boo5bobboo44boo6bo28boo37bobo60bo
30bobbobo3b4obbobo$117bo44b3o46bob5o68bo5boo56b5o25boobob5obb3obb4o$
116boo29boo5boo56b4o37bo31boo5boo57bo29boboo5boo4bo4bo$116bobo29bo5boo
58bo35bo3bo126bo4boboobb3obob3o$148bobo95bo7bo23b5o99b3oboobbo3bobobo$
120boo27boo84bo9bobo3bobo22b3obob3o18boo39booboo35bo4boboo$119boo32boo
78b3o10b5o16bo7bo4bo4bo17bobo37bobobobo22boo12boobobo3b3o3boo$121bo30b
obo78b3o11b3o15boo8bobooboboobo17bo22boo16bobbobo21boo12boobo3bo7bobbo
$124bo28bo35boo41bo3bo6boo3b3o15boo5boobobo3boboboo39bo8b3o8boboo8bo
13bo15b3o9b3o$123boo63bobo16boo24b4o6boo5boo21bobbo7bobbo39bobo8bo7boo
3bo8boo30b4ob4o$123bobo62bo6b3o9bobo10bo12boobo13boobboo18boob7oboo41b
oo7b3o3bobobbobo8boo28boo3bobobo3boo$187boo6boobo10bo9bobo32boo19bo9bo
57boobbooboo37boboobb3obboobo$127boo9boo7boo44boobobo4boo4boo10boo52bo
9bo105bo3bobo3bo$126boo9bobboboobobbobbooboo47bobo24boo3bo37boboo7boob
o103bo9bo$128bo8bobo3boboobb3obob3o38boo7bo24bo3bobo36boo5bo5boo102boo
b7oboo$131bo6boboo5boo4bo4bo46boo10boo12bo3boo39b9o104bobbobo3bobobbo$
130boo8bobooboobboboob4o22boo34bobo13bo40b3obbo3bobb3o101boobobo3bobob
oo$130bobo7bobo3bobbobbobo12bobo9boo35bo13bob5o32boobo3bobbobobbobbo
103boboo3boobo$139boobb3obo4bobbo12boo11bo33boo13boo4bo33boobobo9boo
104bo3b3o3bo$134boo4bobobbob4ob3o13bo64b3o32bo4boboo115b3obob3o$133boo
5bobbobbo4bo78boobo32b3oboobbo3booboo14boo95bo3bo$135bo5boo5boobbo77bo
bo32bo4boboobb3o3b3o11bobbo$126boo10bo8booboo88b3o22boboo5boo4bo4bo7bo
3bobo29boo$125bobbo8boo100bobbo21boobob3obobboboob4o6b6obo21b3o6bo15b
oo43bo$125bobo3bo5bobo103bo4bobo13bobbo5bobboobobo8bo5bo23bo9bo14bo43b
oo$126bob6o105boo7boo16booboboo4bobobbo7boboobobbo22bo24b3o40bobo4bo$
128bo5bo6boo96boo3bo4bo17bobobbob4ob3o9bo3boboo29bo19bo27bobo16bobo$
126bobboboobo5boo91bo10bo22bobbobbo4bo14bobo35bo45boo16boo$126boobo3bo
8bo89bo9bo25boo5boobbo12boo3boo29bobbo45bo21boo$129bobo13bo86b3o5b3o
31booboo12bobboobo32b3o66bobo$126boo3boo11boo49bo11bo32boo47bobbo3bobb
o30b3o61boo5bo$127boboobbo10bobo12boo36bo7b3o32bo48boobo3boboo9bo19bo
bbo9bo51boo5boo$115bo9bobbo3bobbo23bo37bo6bo38bo46boboboobo9b3o19bobo
8b3o$102booboo8b3o7boobo3boboo12boo6boobo38boo4boo33b6o44bobb3obbo8bo
22b3o7bo$96boo5boobbo10bo8boboobobo12boo7bobb4o22bo11bobo38b5o46bobo3b
oboo7boo31boo52bo$95bobbobbo4bo10boo8bobb3obbo13bo7boo3boo22boo10b3o
37bo3bo47bob4obbo93bobo$95bobobbob4ob3o16boobo3bobo16bo6boo24boo13bo
38b3obo48bo3bo7bo75boo10bobo$94boob4o4bobobbo9bo5bobb4obo16boo6bobboo
34boo39bob3o48boboobbobboboboo73boobboo5boobobo$95bobo4boo3bobobbo6bob
o6bo3bo18bobo7boo35boo43bo49boboboo9boo74bobo3bo3boobo$95bob4o4b3ob3ob
oboobboo5bobboobo14boo89b3o8boboo42bobo3bo7bo75bo4boobo3bo$93boboo5boo
4bo4boboo9boobobo14bobbo5boo92boobo41bobbo9boo81bo3b4obo$92bobo3boboo
bb3obob3o14bobo11bobbobbobo4boo18bobbo117boo5bobboo37boo36boo7boo5bobo
$92bobboboobobbobbo3bo16bobo11b5oboboo5bo16bo129b3o38bo38bo8boboboobbo
$93boo7boo24bo18boo3bo6bo13bo3bo54b3o53boo5boo45bobo35b3o9bo4bobo$108b
o34b3obboo8boo13b4o57bo54bo5boo45boo36bo9booboboboboo$108bo33bobobbobo
3bo4bobo54bo17bo55bobo98bobbobobobbo$110b3o29boboobboo49boo14bobo72boo
100bobo3bo$109b5o29bo3boo3bo9boo35boo14boo77boo32boo61boo3boo$108bobbo
boo29booboboo10boo130bobo31bobo64bobo$109b5o31bobobo13bo130bo32bo63b4o
3bo$105boo3boo32bobbobo47boo5boo34boo84boo63bo4boobo$104bobo5bo31boobb
o49bo5boo32b3o95b3o54bo5bo$104bo5boo19bo66bobo36bo4bo93boobo51bob6o$
103boo5boo17bobo67boo36bob6o34boo7boo44boobobo4boobo42bobo3bo$130boo
37boo32boo31boobo5bo32bobboboobobbobbooboo47boboo42bobbo$168boo32bobo
29bo5boboobo32bobo3boboobb3obob3o38boo27boo23boo$170bo32bo30booboobo3b
o34boboo5boo4bo4bo65bobbo$173bo61bobobbobo38bobooboobboboob4o22boo42bo
bo3bo$156bo15boo60bo3bo3boo37bobo3bobbobbobo12bobo9boo44bob6o$155b3o
14bobo26b3o21boo3boobobooboboobbo35boobb3obo4bobbo12boo11bo45bo5bo$
154boobo29boo7boo17boo8bobo3bobo3bobo3bobbo34bobobbob4ob3o13bo56bobbo
bbobo$154b3o19boo8bobboboobobbobbobobo7bo3bo6boobb4obboboobbo3boboo34b
obbobbo4bo73b4obobo$155boo18boo9bobo3boboobb3obob3o4bo4bo5bobboo3bobob
oboboboobobo36boo5boobbo75bobo$177bo9boboo5boo4bo4bo6bo7bobobbo4bo5bo
bb3obbo41booboo73boo3boo$180bo8bob5obb3obb4o3bobbo7booboobo4boo3boobo
3bobo120boboobbo$129b3o47boo8bobo3b4obbobo6boo9bo5bo4bobobbobb4obo109b
o9bobbobobobbo$129bo49bobo6boobb3o4bobobbo9b3o4b4obbo3boo6bo3bo111b3o
7boobo3boboo$130bo58bobobbob4ob3o10boo5bo5bo4bobobbobboobo114bo8boboob
obo$189bobbobbo4bo12boo6booboobo4boo3boobobo114boo8bo3boobbo$148bo41b
oo4b3obbo10boo8bobobbo4bo5bobo125boobo3bobo$149bo48b4o11bo8bobboo3bobo
bo3bobo119bo4bobb5obo$147b3o25boobobo6bo22b3o10boobb4obbobo3bo96bo11bo
10bobobb3obo3bo$124bo49bobb3obo4boo12boo8bo14bobo3bobobo102bo7b3o6boo
bboo4bo3boobo$122b3o48bobo5bo4bobo11bo24boo3booboo103bo6bo9boo9boobobo
$106bo14bo52bob6obo13boobo138boo4boo20bobo$106b3o12boo53bo5bobo5boo5bo
bb4o122bo11bobo26bobo$109bo64bobbobbobobo4boo7boo3boo122boo10b3o26bo$
108boo8boo54b4obobobboo5bo8boo124boo13bo$124bobo50bobo4bo9bo5bobboo
134boo$124bo18boo29boo3boo5bo6boo7boo135boo24bo$109boo64boboobbo3boobb
o3bobo167bobo$109boo12boo3bo14bobo27bobbobobobbobbobobo173boo$123boobo
bo18bo15bo9boobo3boboobobbobo6boo46bobbo66bobbo$125bo19booboboo11b3o9b
oboobobobbooboboo4boo11b4o31bo34b4o31bo$147boobo8boo5bo8bo3boo3bo3boo
3bo4bo10bo3bo30bo3bo30bo3bo30bo3bo$149bo9boo4boo7boobo3b3oboobboo18bo
34b4o31bo34b4o$173bobb5obbobobbobo3bo15bobbo66bobbo63bo$168bo3b3obo4bo
bb3obboo149boo5boo$125boo40bobo3bo3b4o7boo3bo146boo4bobo$125bo19boo16b
oobboo5boobo3b6oboboo$126b3o15bobo16boo10bobobobbobbobbobo80boo$128bo
15bo30boboboo6bobbo77bo3bo$122boo19boo31bo11boo18bo57b6o3boo$122bo84b
oo56bo5bobobbo$123b3o71bo9bobo55bobobbobb3o$125bo51boo5boo10b3o67bobob
3o$112b3o61bobo5bo11boboo11boo55bobobbo108bo$112bobbo59b3o4bobo12b3o
10boo55boo3boo109bo$111bo3bo58b3o5boo13boo13bo53bobboobo108b3o$112bobb
oo57boo3boo34bo48bobbobobobbo$105bo8bo16bo26boo13boo4boo33boo48boobo3b
oboo9bo$105bobo4boo15b3o27boo13boo38bobo48boboboobo9b3o$105boo4b3o14bo
29bo19bo85bobboo3bo8bo$111b3o14boo134bobo3boboo7boo22boo87boo5boo$124b
oo139bob5obbo31bo22boo63boo5bo$123bo143bo3bob3o3bo26bobo21boo67bobo$
124bobo50booboo85boboo3bo3bobo26boobboo16bo20bo48boo$125bo49b3obob3o
84boboboo5boobboo26boo35b3o44boo$174bo4bo4bo85bobo10boo62bo47bobo$174b
obooboboobo84bobbo59boo13boo14boo31bo$172booboboobooboboo38boo43boo59b
oo30boo$172bobbo3bo3bobbo37boo55boo49boo62bo$173boob7oboo40bo36boo5boo
8boo51b3o60bo$174bo9bo44bo34bo5boo10bo26bobo23bo33boo$174bo3bobo3bo43b
oo34bobo41bobbo23b4o25bo4boo13bobo7bo3bo$126boobbooboo37boboobo3boboob
o41bobo34boo41bo3bo24boo24b3o18boo6b3o3b3o$111boo13bobobbobo38boo11boo
82boo37bobo25b3o16boo5b3obo18bo5bo3b3o3bo$88bo21bobo8bo7boo3bo6bo14bob
o16b9o48boo34bobo41boo21bobo15boobbo33boboo3boobo$87bo22bo9bobo7boboo
7boo13boo14b3obbo3bobb3o44boo36bo35bo7bo21bo3bobbo10bobb3o30boobobobob
oboboo$87b3o19boo8booboo3bobbobo7bobo14bo10boobo3bo3bo3bobbo46bo70bob
oobobbo10boo11b6o11bo4bo30bobbobobobobobbo$119bobbo3bobobobo36boobobo
4bo4boo118bo5b3o10bobo9boobboo13b5o5b3o3boo18boobo5boboo$118bo3bo4boob
oo35bo4boboo92b3o32boo20bo30boo4b5o3boo19bo3bobo3bo$122bo42b3oboobbo3b
o3bo72boo7boo54boo4boo8bo26booboo24bo9bo$147boo15bo4boboobb3obob3o69bo
bboboobobbobbobobo47bobo14b3o7boo3bo12bo24boboobb3obboobo$68boo5boo60b
oobbobo3bobob3o10boboo5boo4bo4bo68bobo3boboobb3obob3o7bo39bo14b3o7bo3b
obo36boo3bobobo3boo$69bo5boo59b3obo3bobbobo13boobob4o4b3ob4o70boboo5b
oo4bo4bo7boo28boo7boo10boo12bo3boo39b3o3b3o$69bobo63boo6bo3b3o13bobbob
o4boo3bobo75bob5obb3obb4o7boo29boo18bobo13bo40b3o9b3o$70boo64bob5o3bo
3bo14boob4o4bobobbo61bo12bobo3b4obbobo61bo13bob5o11boo19boobo3bo7bobbo
$74boo46bo14b4o4bo4bo15bobobbob4ob3o61boo11boobb3o4bobobbo27bo31boo13b
oo4bo11boo20boobobo4bo4boo$73bobo45boo16bo6bo3bo15bobbobbo4bo19bo44bob
o11bobobbob4ob3o27boo49b3o32bo4boboobb3o$74bo43bo28bo19boo5boobbo17b3o
57bobbobbo4bo30bobo45boobo32b3oboobbo3bobobo$117bobo53booboo17boobo47b
oo9boo5boobbo77bobo19bo12bo4boboobb3o3b3o$74bo37boo3bobbo6boo66b3o47b
oo16booboo98boo13boboobo3boo3boo4bo$74bo37boo6bo16boo57boo49bo119boo
11boobob3obobboboob4o$117bobbo15bobo13boo96bo129bobbo5boobobbobo$72bo
3bo7bobo29bobbobboo14bo14bo95boo100bo30boobb3o4bobobbo$70b3o3b3o6boo
30boo3boo28bo96bobo99bobo29bobobbob4ob3o$69bo3b3o3bo5bo30boo34boo197b
oo3b3o24bobbobbo4bo$69boboo3boobo36boo238bobbo24boo5boobbo$67boobobobo
boboboo34boo5boo229bo4bo30booboo$67bobbobobobobobbo41boo187bo10bo$68b
oobo5boboo188boo39b4o7b3o29bo5bo$69bo3bobo3bo189bo28bobo9b4o6bo$69bo9b
o186boobo29boo19boo32boo4bo$67boboobb3obboobo184bobboobo26bo56boo3bo$
67boo3bobobo3boo178boo5boo3bo37b4o43bo3bo$70b3o3b3o180boo8boobo37b3o
47bo$67b3o9b3o179bo7bobo39bo42boo3boo$67bobbo7bo3boboo178bo8bo80b3o$
68boo4bo4boboboo51boo119boo4boo7bo82bo9boboo$73b3obboobo4bo47b3o119bo
bbo3bobo99boobo$72bobobo3bobboob3o30b3o11bo4bo112bobbobbobo$70b3o3b3o
bboobo4bo12bo18bo11bob6o110b5oboboo6boo25b4o36bo$69bo4boo3boo3boboobo
13boo15bo11boobo5bo115bo3bo4boo26bo3bo34bo$70b4oboobobbob3oboboo11boo
26bo5b4obo111boobo4bo6bo25bo38b3o$73bobobboboo5bobbo39booboobobobo111b
o3boo3bo33bobbo47boo$72bobbobo4b3obboo42bobobbobo113bobobo4bo53boo28bo
bo22boo$73b3ob4obobbobo42bo3boboboo113bo3bo3bo53boo30bo21bobbo$76bo4bo
bbobbo33boo3booboboobo5bo113booboboo108bobo3bo$75bobboo5boo34bobo3bobo
3bobobobobbo112bobobo110bob6o$76booboo38boobb4obboboobboboboboo93boo
16bobbobo53boo5boo50bo5bo$118bobboo3bobobobobo4bobo93bobbo15boobbo55bo
5boo48bo4boobo$118bobobbo4bo5boboboobbo92bobo3bo36bo35bobo53b4o3bo$
106boo9booboobobboboo3boobo3bobo24boo67bob6o33boo36boo56bobo$106boobb
oo5bo3bobobobbo7b4obo24bobbo27bo40bo5bo32bobo39boo49boo3boo$110bobo5b
3oboo4boboobboo3bo26bobo3bo23b3o37bobb4obo73bobo50bobo3bo$111bo5bo3bob
obobbo7boobo27bob6o21boboo36boobobobo75bo39bo9bobbobobobbo$117booboobo
bboboo3boobobo30bo5bo21b3o39bobo117b3o7booboboboboo$108boo8bobobbo4bo
5bobo30bobboboobo21boo37booboboo119bo8bo4bobo$91booboo3boo8bo8bobboo3b
obobo3bobo30boobo3bo62bo5bo41bo75boo8boboboobbo$90bobobo3bobo5b3o6bo3b
oobb4obbobo3bo34bobo52bo9bobbobobobbo38boo17boo7boo14bobo39boo5bobo$
86bo3bobobb4obboo3bo6b3o5bobo3bobobo35boo3boo38booboo8b3o7booboboboboo
38bobo15bobboboobobbobb5o8boo8bo24bo4bo3b4obo$85bobo3bobobo3boobbo8bo
8boo3booboo37boboobbo31boo5boobbo10bo8bo4bobo57bobo3boboobb3obob3o6bo
8bobo22bobo3boobo3bo$85bobo5bo3boobbobo8boo42bo9bobbo3bobbo28bobbobbo
4bo10boo8boboboobbo57boboobo3boo4bo4bo14bobo18boobboo4bo3boobo$83bobob
oo4boo5booboo38booboo8b3o7boobo3boboo28bobobbob4ob3o16boobo3bobo59bob
ooboobb4ob4o3boo9boobobo16boo9boobobo$82boboobbo7bo3bobobbo4bo26boo5b
oobbo10bo8boboobobo28boobb3o4bobobbo9bo8b4obo60bobo4boobobobo6boobboo
8boobo27bobo$82bo3b3o7bo3boobb3obbobo24bobbobbo4bo10boo8bobb3obbo28bob
o3b4obbobobbo6boboboobboo3bo61boob4obobbobobbo9boboboobboo3bo27bobo$
80bob4obbo7bo3bobobbo4boobboo20bobobbob4ob3o16boobo3bobo28bob5obb3obb
3oboboobboo8boobo62bobobbob4ob3o11bo8b4obo15boo9bo$79bobo3boboo4boo5b
ooboo9boo19boob4o4bobobbo9bo5bobb4obo27boboo5boo4bo4boboo9boobobo63bo
bbobbo4bo20boobo3bobo13bobo$79bobb4obo5bo3boobbobo32bobo4boo3bobobbo6b
obo6bo3bo29boo3boboobb3obob3o14bobo26bo39boo5boobbo10boo8boboboobbo15b
o$80bobobbobobobobobo3boobbo32bob4o4b3ob3oboboobboo5bobboobo32booboobb
obbobobo16bobo25b3o27boo15booboo12bo8bo4bobo$79boobobobobboobobb4obboo
31boboo5boo4bo4boboo9boobobo34bo4boo18bo5bo26boboo25boo30b3o7boobobobo
boo$79bobb3obobo3bobo3bobo32bobo3boboobb3obob3o14bobo34bobo9b3o10bobo
33b3o27bo29bo9bobbobobobbo$81bo3bobobooboboo3boo32bobboboobobbobbo3bo
16bobo34boo24boo33boo70bo5bo$82boobobo3bo42boo7boo24bo167booboboo$83bo
4bobo58bo69bo120bobo$81bobob4oboo57bo68bobo116boobobobo$80bob4o5bo10bo
48b3o65boo81boo33bobb4obo$80bo5boboo11bo17boo29b5o60boo84boo36bo5bo$
81b6obo12b3o14boo29bobboboo58bobo86bo33bob6o$83bo4bo31bo29b5o59bo5boo
114bobo3bo35bo$85b3o58boo3boo60boo5boo114bobbo39boo$84boo59bobo5bo183b
oo39boo6boo5boo$145bo5boo19bo213boo5bo$144boo5boo17bobo58boo158bobo$
171boo58bobo109b3o45boo$231bo113bo41boo$313bo30bo42bobo$249bo62boo74bo
$197bo52bo61bobo$196b3o49b3o149boo$195boobo189bo10bobo$195b3o189b3o3b
oo4bo$196boo188bobobobbobbooboo$320bo63b3o3b3obboobo3boo$84bo52bo181b
oo62bo4boo3boo3boboobo$84bobo49boo32b3o146bobo62b4oboobobbob3obo$84boo
50bobo31bo138boo61bo14bobobboboo5bo$68boo5boo94bo138bo60bo14bobbobo4b
3obboo$69bo5boo233bobo58b3o13b3ob4obobbobo$69bobo117bo44bo76boo77bo4bo
bbobbo$70boo48bo42bo26bo41b3o81bo72bobboo5boo$74boo44b3o38b3o24b3o25bo
14bo16b3o64bobo8boo62booboo$73bobo47bo16boo18bo55b3o12boo15bo65boobo7b
obo$74bo31boo14boo11boobb3obboo14boo57bo24bo4bo16bo47bobo10bo$106boo
27bobbobo4boo71boo17boo3bo3bo18b3o46bobo$74bo61bo3boboobo90b3o3bo21boo
bo44bobboo$74bo64bo3boo92bo3bo5boo15b3o49bo$100boo117boo19boo6bo16boo
48bo$72bo3bo23boo63bobo51boo27bo66bo$70b3o3b3o25boo59bo18boo52bo5boboo
64bobo$69bo3b3o3bo24boo12bobo117boobbo71bo$69boboo3boobo8bo21bo7bobobo
41boo3bo14bobo53boo27boo55boo9boo$67booboboboboboboo7boo18bobo11boo39b
oobobo18bo80boo35boo5b3o10bo9boo$67bobbobobobobobbo6boo32bo23boo18bo
19booboboo34bo77bobo16bobo11bo$68boobo5boboo18boo44bobo40boobo8boo24b
3o76bo18boo28bo$69bo3bobo3bo19boo44bo44bo9boo23boobbo5boo67boo48bobo$
69bo9bo52boo10boo10boo71bo5bo19boo97boo$67boboobb3obboobo37bo3boo32bo
52booboobboo9bo7b3o15bobo52boboo$67boo3bobobo3boo36bobo3bo29b3o9boo43b
obobbobo5bo13bo15bo52b3oboo$70b3o3b3o39boo3bo12boo16bo11bo19boo22bo3b
oo8bobo5boo19boo51bo$67b3o9b3o40bo13bobo28bo17bobo23boobo9boo6bo74b3ob
oo$67bobbo7bo3boboo32b5obo13bo27boo17bo26bobobbo15b3o73bobo6b3o18bo$
68boo4bo4boboboo33bo4boo13boo44boo25bobbobobo16bo73bobo6bobbo16bobo$
73b3obboobo4bo32b3o70bo9boo5bobb3oboo92bo6bobboo16bobo$72bobobo3bobboo
b3o23b3o6boboo66bobo7b4o4b3o19boo84boo17boboboo9boo$70b3o3b3obboobo4bo
22bobo7bobo67bo7bo4bo6bo17b4o101boboo3bo4boobboo$69bo4boo3boo3boboobo
21bobbo84boo4boo4boo16bo4bo21boo55boo6bo13bo3bob3obbobo$70b4oboobobbob
3oboboo20b3o76b5o4boo4boo21boo4boo19bobbo53bobo7boo9bob5obbo4bo$73bobo
bboboo5bobbo20b3o71boobbo4bo5bo4bo22boo4boo19bobo3bo50bo8boo9bobo3bob
oo$72bobbobo4b3obboo16bobo4bobbo69bobbobbo9b4o24bo4bo21bob6o47boo19bo
bboo3bo8boo$73b3ob4obobbobo18boo4bo73boboboo10boo9boo15b4o24bo5bo68bob
oboobo8bo$76bo4bobbobbo18bo8bo69boobo5bo16b3oboo14boo23bobboboobo67boo
bo3boboo7b3o23boo$75bobboo5boo35bo65bo4bobo15boboboo39boobo3bo68bobbob
obobbo9bo22bobbo$76booboo42bo64boobbobbo13boobo46bobo72bobboobo34bobo
3bo$121b3o69boo61boo3boo66boo4boo3boo34bob6o$208bo16boo30boboobbo41bo
23bobo4bobo39bo5bo$110boo112bobbobboo23bobbo3bobbo39b3o23bobbobob4o34b
obbobbobo$224bobo4bobbo10bo9boobo3boboo42bo22bobobobbobbo34b4obobo$
225bo5bobobo9b3o9boboobobo42boo14boo5boobo5bo39bobo$228boobobbo13bo8bo
bb3obbo57boo9b6obo34boo3boo$111bobo94bo3boo14bobbo15boo7boobo3bobo70bo
3bobo34boboobbo$112bo94bobo3bo11bo4bo25bobb4obo74bobbo32bobbobobobbo$
111bo83bo11boo3bo12b5o20bo7bo3bo56bo20boo23bo9boobo3boboo$102boobo9bo
77b6o12bo37bobo4bobboobo55b3o44b3o9boboobobo$102boboo9bo77boobboo8b5ob
o13boobo14boobboo5boobobo55boobbo46bo8bo3boobbo$207bo4boo13boboo14boo
10bobo61boo44boo7boobo3bobo$119b3o75bo6booboboo46bobo58b3oboo51bobb5ob
o$119bo73boobbo6boboboboboo44bo60bobboo47bobb3obo3bo$120bo72boo3bo7bo
4bobo104b3o48bobo3bo3boobo$197bo8boo38boo73boo42boobboo5boobobo$140bo
54bobo49boo10boo5boo22boo29boo42boo10bobo$138bobo55bo49bo12boo5bo22bo
bbo31boo51bobo$139boo123bobo22bobo3bo28bobo44bo6bo$264boo24bob6o16bo
11bo45bo$149boo5boo102boo30bo5bo15bobo9boo42b3o$149boo5bo56bo46bobo27b
obb4obo15boo63boo5boo$154bobo54b3o47bo28boobobobo81boo5bo$154boo54bo
82bobo88bobo$150boo42boo14boo62boo14booboboo87boo$150bobo41boo65bo11bo
bbo14bo5bo82boo$151bo99bo8b3o3boo6b3obbo9bobbobobobbo33bo46bobo$181bo
67boo8bobobobbobbob3o5b3o7booboboboboo31b3o47bo$181bobo66boo5b3o3b3obb
oobo3boo5bo8bo4bobo31bo$137boo42boo73bo4boo3boo3boboobo4boo8boboboobbo
14boo14boo$137bobo17boo7boo89b4oboobobbob3obo15boobo3bobo14boo3bo$131b
o5bo12b5obbobboboobobbo91bobobboboo5bo9bo8b4obo19b3o65boo7boo$130bobo
15b3obob3obboobo3bobo60bo29bobbobo4b3obboo7boboboobboo3bo20booboo57boo
boobbobboboobobbo$130bobo14bo4bo4boo3boboobo31boo28boo28b4ob4obobbobo
4boobboo8boobo24bo31boo22b3obob3obboobo3bobo$128boboboo9boo3b4ob4obboo
boobo32bobo27bobo21booboo6bo4bobbobbo4boo9boobobo58boo20bo4bo4boo5boob
o$127boboo8boobboo6boboboboo4bobo31boo52bobboo5boobb3o4boo17bobo25bo
33bo23b4oboobobbooboobo$127bo3boobboobobo9bobbobobbob4oboo32bo8boobboo
boo35bo4bobbobboo26bobo3bo20boo45bobo12bobobbobbo3bobo$125bob4o8bo11b
3ob4obobbobo27boo4bobo6bobobbobo33b3ob4obobbobobboo24bo3bo21bobo44boo
12bobbo4bob3obboo$124bobo3boboo20bo4bobbobbo26bobo6boo8boo3bo31bobbobo
4b3obbo3bo12boo14b3o67bo13b3ob4obobbobo$124bobboobobo8boo10bobboo5boo
27bo7b3o9boboo33bobobboboo5bobo13bobo34bo66bo4bobbobbo$125bobo4bo8bo
12booboo32boo16bobbobo31b4oboobobbob3oboboo14bo34boo64bobboo5boo$124b
ooboboboboo7b3o63bobobobo30bo4boo3boo3boboobo51bo10boobbooboo46booboo$
124bobbobobobbo9bo64booboo32b3o3b3obboobo4bo47boo13bobobbobo$126bo5bo
115bobobo3bobboob3o47bobo16boo3bo$127booboboo30bo67bobo14b3obboobo4bo
49bo19boboo$128bobo19boo5boo4bo46boobboo16boo10boo4bo4boboboo50boo16bo
bbobo$126boboboboo17bo5boo4b3o48b3o16bo9bobbo7bo3boboo62bob3obobobo$
125bob4obbo17bobo55bo33b3o9b3o67b3obooboo$125bo5bo20boo62bobo6boo4boo
13b3o3b3o70bo$126b6obo22boo51bobbob4o6bobo4boo10boo3bobobo3boo39bo$
128bo3bobo20bobo52b3ob3o9bo16boboobb3obboobo40boo36bo16b3o$131bobbo21b
o88bo9bo41boo37boo14b4o$132boo111bo3bobo3bo79bobo13boobboo$194boo48boo
bo5boboo95boboo$194boo47bobbobobobobobbo21bo45b3o25b3o$141boo7boo48boo
32boo7booboboboboboboo21bobo42bobobobo23bo$140bobboboobobbobb5o41boo
33bo9boboo3boobo6b3o14boo43bo3boboo$140bobo3boboobb3obob3o73bo10bo3b3o
3bo8bo59boobbobo$141boboobo3boo4bo4bo72boo10b3o3b3o8bo50boo10bo5bo$
143bobooboobb4ob4o37boo48bo3bo61boo10bobboboo$143bobo4boobobobo40boo5b
oo113boo5boboo23boo$142boob4obobbobobbo46boo43bo69boo33bo$143bobobbob
4ob3o14bobo75bo103bo$143bobbobbo4bo18boo179boo$144boo5boobbo17bo76bo
67boo29boo$150booboo94bobo66boo5boo20b3o$207b3o40boo73boo5boo12bo4bo$
209bo36boo66bobo14bobo12bob6o$208bo36bobo67boo16bo11boobo5bo$245bo5boo
62bo27bo5bobbobo$218boo24boo5boo90boob4obobo$216b3o43bo81bobobbobo$
215bo4bo40bo81bo3bo3boo$215bob6o30bo7b3o70boo3boobobooboboobbo$214boob
o5bo28bobo79bobo3bobo3bobobobobbo$212bo5b4obo28bobo10boo65boobb4obbob
oobbo3boboo$212boob4obobo27boboboo5boobboo64bobboo3boboboboboboobobo$
213bobo4bo28boboobbo4bobo68bobobbo4bo5bo3boobbo$212bo3boboboo27bo3b3o
5bo57boo9boob3o4boo4boobo3bobo$190bo12boo3booboboobobo3bo24bob4obbo63b
oobboo7bo4bobo5bobb5obo$191boo10bobo3bobo3bobob3obbo21bobo3boboo7boo
58boboboo3boboo3boo3b3obo3bo$190boo9boobb4obboboobboboboboo21bobb4obo
8bo60bo7bo4bobo5bo3boobo$200bobboo3bobobobobobobbobo23bobobbobo9b3o63b
oob3o4boo4boobobo$200bobobboo3bo5bob4obbo21booboboboboo9bo54boo8bobobb
o4bo5bobo$188boo9booboo5boo4boobo3bobo21bobb3obobbo65bo8bobboo3bobobo
3bobo$188boobboo4bobbobo3bo7bobb4obo24bo3bobo64b3o10boobb4obbobo3bo$
192bobobb3obboo3bo7b3o3bo27booboboo63bo14bobo3bobobo$193bo4bobbobo3bo
7bobboobo28bo4bo78boo3booboo$199booboo5boo4boobobo27bobob3o$190boo8bob
obboo3bo5bobo28bob4obb3o$191bo8bobboo3bobobo3bobo28bo5bobobbo$188b3o
10boobb4obbobo3bo30b6o3boo$188bo14bobo3bobobo36bo3bo$203boo3booboo40b
oo!

Yeah to all you said, sorry - like I said, I'm a noob with this stuff so I'm not yet quite familiarised with terminology, but I hope what I said was nevertheless understandable. I feel especially dumb for using the c for transmission rate. >.<

Oh well, I'll learn.

edit: Ah, by the way, it's nice to see that reading an LWSS stream at period-14 is possible. :)
doccolinni
 
Posts: 25
Joined: May 18th, 2010, 11:36 pm

Re: Spaceship speed limits

Postby Phantom Hoover » May 20th, 2010, 1:13 pm

However, most technology runs at either p30 or p46 or is stable, so you wouldn't be able to process the data fast enough.
Phantom Hoover
 
Posts: 20
Joined: May 16th, 2010, 3:54 pm

Re: Spaceship speed limits

Postby doccolinni » May 20th, 2010, 1:56 pm

Phantom Hoover wrote:Allow me to clarify this to you. Information cannot travel more than 1cell/generation in Life. It is incredibly obvious; it derives from the axioms of Life. This is not a "philosophical" matter; it is hard mathematical reality. The Stargate does not send information at 15c/14; this is an illusion that derives from your godlike, three-dimensional observer status, able to instantly see the state of every cell in the universe.

Okay, maybe not at over the "speed of light" in the Life space, but the Stargate definitely transmits information faster than an LWSS stream at period-30 does on its own. It doesn't do it at 15/14, but it definitely is over 1/2. That is yet even more proof of the fact that the Stargate is completely useless, because LWSS stream at period-14 now definitely transmits more data per generation than an LWSS stream at period-30 "assisted" by the Stargate, despite the speed-up.

Yes, from your explanation now it's obvious that nothing in Life space can travel faster than 1cell/generation, I can't believe I actually presumed Stargate did transfer data at 15/14...

Sleep deprivation, I tell ya. :P
doccolinni
 
Posts: 25
Joined: May 18th, 2010, 11:36 pm

Re: Spaceship speed limits

Postby calcyman » May 20th, 2010, 2:31 pm

... the Stargate is completely useless ...


It's not completely useless at all: it's fun to see how many people fall for the trap of thinking that it performs the impossible. :D


Anyway, Jason Summers has constructed a device to transmit information at lightspeed orthogonally, and I have produced a stable version. So, the Stargate is not ideal for practical signal acceleration, as there are much more effective ways of transmitting information at high speeds. Dave Greene and Noam Elkies' 2c/3 transceiver is another pattern that transmits information at a supervacual rate.
What do you do with ill crystallographers? Take them to the mono-clinic!
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calcyman
 
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