Date: Wed, 11 Jun 1997 13:56:33 -0400
From: (Noam Elkies)
Subject: p24 gun, finally!

On Nov.29, 1994, RWG wrote about his p24 oscillator:

>Someone will make a gun from this within 24 hrs. [...]

This was off by three orders of magnitude: it was more like 24 months, and required a special-order p4 courtesy of DRH's improvement of David Bell's search program (thanks, Dean!). The mechanism is not the one generating a glider directly with the assistance of a vertical spark, but a more complicated one where two p24's interact with the assistance of a couple of sparks. Unable to fit two sparkers to provide them separately, I finally tried for a single hybrid p4 to supply both the one-cell spark a la mold and the domino spark one generation later, and after several day-long searches reached an end that I could finish off by hand with a pair of toads (as shown here) or eaters. The resulting oscillator is an ugly beast that dwarfs the rest of the construction, and can probably be reduced considerably (quite aside from whittling down the stator), but at least it works. Here's the complete gun; the glider barely escapes past the eater on the left, but if came too close this eater could be replaced by a figure-8 to delete the extraneous blinker.


--Noam D. Elkies

Date: Fri, 13 Jun 1997 11:08:57 -0400
From: (Noam Elkies)
Subject: p72 guns

Is there a known gun of period 72 other than the huge ones obtained from Herschel loops? I tried unsuccessfully to produce one by applying a p72 spark to the p24 oscillator. But now that we have a p24 gun we can use the p72 to *delete* every third glider. Doing this once yields an intermittent gun of period 72 (which the Herschel guns don't do, though I suppose the insertion reactions can manufacture it from several such guns, and aren't restricted to a separation of 24); of course two p72's can thus be used to get a p72 glider stream, but it turns out that a single p72 suffices to thin a p24 glider stream by a factor of three. Pictures of both follow.


From: Paul Callahan
Date: Fri, 13 Jun 1997 21:09:39 +0200 (MET DST)
Subject: Re: p24 & p48?

The p24 LWSS gun can be turned on and off by deleting appropriate gliders. In the off state, two gliders destroy each other and the third can be eliminated with an eater. Here's the reaction showing 3 colliding streams of 6 gliders each:

The glider stream produced by the LWSS/glider collision can be turned on and off in a similar fashion by deleting the glider to turn it off, and the deleting the LWSS to turn it back on.


From: "David I. Bell"
Subject: Period 24 MWSS gun and other stuff
Date: Sat, 14 Jun 1997 19:42:14 +1000

(Geeze, it seems that some people never look at the stuff I send in:)

If people had looked at what I sent in a week or so ago on c/3 puffers, they would have seen a LWSS to MWSS convertion reaction found by Dieter Leithner a long time ago. The same reaction used there easily makes a MWSS stream using three LWSS streams:

Dieter also had a similar smashing reaction which turns MWSS's into HWSS's, so you can probably make a period 24 HWSS gun from it. Someone should go back and check whether his reaction works here. (I don't feel motivated enough today to do it.)

Colliding two p24 glider streams can produce several period outputs, including period 72 and 96. The period 72 is a two-on one-off, and so isn't too wonderful considering the p72 gun shown today. The p96 gun is real nice, though:

Finally, the on-off LWSS gun reaction is old news. I found a similar reaction for p30 LWSS streams a long time ago.

BCNU, -dbell-

From: "Dieter Leithner"
Date: Mon, 16 Jun 1997 09:48:21 +0200
Subject: Re: p24 & p48?

Mostly to Noam:

Congratulations on the fastest genuine glider gun yet! It is wonderful to finally have it, especially for gun collectors.

Your ingenious period-doubling mechanism (p48 glider gun) started me to look for other such p24-specific multipliers. Two were easy to find, yielding gun periods of 3 x 24 = 72 and 4 x 24 = 96:

p72 glider gun based on Noam Elkies' p24 glider gun

p96 glider gun based on Noam Elkies' p24 glider gun

You said:

> Still there should be also a way to use p24 glider streams and
> p24 oscillators to produce p24 spaceship guns; any ideas?

All types of p24 spaceship guns can be constructed with your new glider gun. First build a p24 LWSS gun using the fast synthesis of a LWSS by 3 gliders (as Paul already has pointed out). Then hammer on the p24 LWSS stream with two other p24 LWSS streams to make a p24 MWSS stream. Finally, hammer on the p24 MWSS stream with four p24 glider streams to transform it into a p24 HWSS stream. Fortunately, these three basic mechanisms work fast enough for p24:

3 gliders -> LWSS (p >= 23)

3 LWSS -> MWSS (p >= 17)

MWSS + 4 gliders -> HWSS (p >=22, found by Peter Rott)

The sizes of the p24 MWSS and HWSS guns built in this way are rather large. Hopefully, smaller guns can be found which use additional oscillators as you suggested. In contrast, all three types of p48 spaceship guns are reasonably sized. Each can be constructed with only four copies of the p24 glider gun:

p48 LWSS gun based on Noam Elkies' p24 glider gun

p48 MWSS gun based on Noam Elkies' p24 glider gun

p48 HWSS gun based on Noam Elkies' p24 glider gun


PS: While quickly scanning my mail this morning I saw that David Bell (David, I always read your mail!) apparently has sent the same or similar stuff to the above. As I have to wait until tonight for time to study my mail in detail, I am sending this note as prepared yesterday.

From: Dean Hickerson
Date: Tue, 17 Jun 1997 23:26:41 -0700 (PDT)
Subject: Period 24N guns, N=11, 12, 14

Dieter said (to Noam):

> Your ingenious period-doubling mechanism (p48 glider gun) started me to
> look for other such p24-specific multipliers. Two were easy to find,
> yielding gun periods of 3 x 24 = 72 and 4 x 24 = 96:

Here are 3 more, based on a 3- collision, with periods 264, 288, and 336. I think that the p336 is the smallest known gun of its period; the others are not.

The p288 and p336 use the blinker eater that I found in April. I couldn't find a way to use a conventional eater there, but I may have missed something.

It's likely that other periods can be obtained by changing the reactions that occur along the SWward glider stream. (Paul: Is this something that your search program could look for?)

p264 gun using 2 p24 guns

p288 gun using 2 p24 guns

p336 gun using 2 p24 guns

Dean Hickerson

Date: Fri, 20 Jun 1997 02:57:12 -0700 (PDT)
From: Dean Hickerson
Subject: Period 24*8=192 and 24*9=216 guns

Here are a p192 gun and a p216 gun based on a 4- collision. I think they're the smallest known with those periods.

p192 gun using 2 p24 guns

p192 gun using 2 p24 guns

Dean Hickerson

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