Crystal based sawtooth?

[gmc_nxtman]

I was thinking that somebody could make a very small sawtooth by combining the glider crystal reacton, and the very similar reaction which causes the gliders to turn against it. All we need is a spaceship capable of starting up the glider crystal moving at a speed of c/5 diagonal or slower, and a catalyst capable of "inverting" the crystal. Anyone up to it?

[Kazyan]

It would be pretty easy to damage the crystal so as to put it back in the state where a glider stream tears it down instead of building it--there's a pattern that comes with Golly that demonstrates this--but after you tear it down, there are still going to be gliders en route, assuming a standard glider gun. Since the ship keeps getting further away, the root of the crystal will keep being further away as well, so the number of en route gliders will increase...

It might work to use a caber tosser, so as to exponentially space out the glider stream so that there will only be a fixed amount en route at a time (I'd need to build that to make sure it works), but we'd need one of about 100 cells or lower in its minimal phase to beat out Sawtooth 181.

[gmc_nxtman]

Perhaps you misinterpreted my idea. In my scenario, there would be no need for external timing due to the eating reaction, which would last for a while, but still technically be a sawtooth. Here is a diagram.

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#C [[ VIEWONLY ]]
x = 66, y = 59, rule = LifeHistory
44.2A$44.2A$43.A2.A$43.A2.A.2A$43.A$43.A2.A3.2A$44.A5.2A$44.5A.A$49.A
3$50.3A$52.A$53.2A$54.A4.2A$54.A3.3A$46.D10.A4.A$45.D.D10.A3.A$45.D.D
10.A$46.D11.A.A.2A$58.A5.2A$58.2A4.2A$3D.2D2.D.D.D.3D.3D.3D17.2D16.4A
$.D2.D.D.D.D.D.D3.D.D2.D17.D2.D$.D2.D.D.D.D.D.3D.2D3.D18.2D$.D2.D.D.D
.D.D.D3.D.D2.D14.D$3D.D2.2D.3D.3D.D.D2.D13.D.D$37.D.D$38.D2$11.D22.2C
$11.D2.D18.C.C$11.D3.D19.C$12.2D2.D.2D$15.D2.2D$14.D13.2C$27.C.C$29.C
4$23.2C$22.C.C$24.C$11.2D$11.2D3.D.D7.2D$17.D.D5.D$17.D.D5.D6.2D$16.D
.D7.2D4.2D6$16.3D.D.D.2D2.D$16.D3.D.D.D.D.D$16.D.D.D.D.D.D.D$16.D.D.D
.D.D.D.D$16.3D.3D.D2.2D!

On another note, I found a candidate for a crystal activation mechanism. If only there were a ship that could survive this reaction........!

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x = 58, y = 61, rule = B3/S23
36b3o$39bo$36b2o2bo$36b2obob2o$36b2o2bo2bo$37bobo3bo$38bob2obo$40bobo$
39b4o$39b5o$39bo3b2o$42bo2bo$43bo2bo$47bo$45bob2o2b3o$46bob3o3bo$48b2o
bo2bo$48b4obobo$47b3o2bobobo$51bo5bo$52b4obo$53b3obo19$24b2o5b2o$24b2o
5b2o2$27b2o$27b2o$22b3o$22bob2o$23bob2o$4b2o17bobo$4b2o12bo4b2o$18bobo
$2o5b2o9b2o$2o5b2o7$4b2obo$4bob2o!

[calcyman]

Perhaps you misinterpreted my idea. In my scenario, there would be no need for external timing due to the eating reaction, which would last for a while, but still technically be a sawtooth. Here is a diagram.

I believe Kazyan is right, unless I'm still misinterpreting your idea. The definition of a sawtooth is that the liminf* of the population is finite. What you describe is bounded below by a (linear) increasing function, so is not a sawtooth.

* https://en.wikipedia.org/wiki/Limit_sup ... t_inferior

Kazyan's modification (the use of a caber tosser) would yield a valid sawtooth, but is too complicated to have a population below 181.