Introduction to me and my findings in cellular automata

[psyklon]

Hello,
this is my first post here, so altrough I read trough the guildelines and a few other posts, please be kind and point me in the right direction if I ask a silly question.

I'm interested in generative art, and more generally in the field of fractals since my late childhood, but only recently I started to deeply examine the beutiful world of cellular automata. I was already familiar with Wolfram rules and the fact how simple they are. Every permutation has a single value in binary, encoding how it will evolve. I searched if it was already implemented in 2D cellular automata with no luck, so I started scripting to see if it works. As it turned out later - when I refined my search keywords - it was already described in the MAP rules section of this page.

After this, with the tools ready in my hand, I quicky realized that not only Game of Life, but even Wolframs rules can be simulated with these rule tables, so i created converters (screenshot). Soon I developed a simple rulemaker application too (screenshot), and carefully hand-crafted a rule specifically for implementing the simplest possible glider gun.
(The application will be published online, but the whole thing is in a very early and messy state now)

We must stop here for a second, I have a - possibly silly - question... Is a single pixel can be considered a glider?

If you take a look at my profile picture, I think you already realized why I ask this. Because if it is, then the picture on the right is the smallest glider gun ever built, by only 2 live cells at its smallest evolution.

What do yout think?

[GUYTU6J]

Welcome to the forums!

Yes, a single cell can be said to be a spaceship in certain anisotropic rules. No, the smallest known spaceship gun in terms of population has only 1 cell, achieved in these two (EDIT: three, I missed one) isotropic rules:

Two rules where a single cell is a gun:
P6:

Code: Select all

x = 1, y = 1, rule = B1e4aew8/S01e3iy4at5a6c
o!

P7:

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x = 1, y = 1, rule = B1e4acew/S01e3iy4at5a6c
o!

New highest-period 1-cell gun, p8:

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x = 1, y = 1, rule = B1e3e4aew5k8/S01e2n3iy4at5a6c
o!

[psyklon]

No, the smallest known spaceship gun in terms of population has only 1 cell

Woah, thanks for the heads up! The one I can find via google is a 4 cell gun in Sayab rule, but it was from a 2017 paper.

EDIT: So as I understand, the challenge here now is to find a highest period 1 pixel gun, right?

EDIT2: Challenge accepted! Thanks to your comments and my rulemaker, it wasn't that hard to come up with this period-9 single cell glider gun!

Code: Select all

x = 1, y = 1, rule = B1e4acew5e/S01e3iy4at5a6c
o!

[yujh]

welcome! here is a p10 gun for you

Code: Select all

x = 1, y = 1, rule = B1e4acew5ek/S01e2ik3iy4act5a6c
o!

[psyklon]

welcome! here is a p10 gun for you

Code: Select all

x = 1, y = 1, rule = B1e4acew5ek/S01e2ik3iy4act5a6c
o!

Wow, great example! Let's see how far can we get!

I don't know if this can be considered a "true" glider gun, because it seems kind of "dirty". The very first glider it emits does not exactly look like the others. However, after the first few steps the gun stabilizes at a constant period of 13.

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x = 1, y = 1, rule = B1e4awec5ke/S01e2ki3iy4aitc5a6c
o!

[yujh]

The gun is a true gun as opposed to pseudo gun, which has a period that is a multiple of the period of the output spaceship stream, like this one.
However, this gun does not have a population of one as a dot is just a predecessor of the 5 cell p13 gun.

[psyklon]

The gun is a true gun as opposed to pseudo gun, which has a period that is a multiple of the period of the output spaceship stream, like this one.
However, this gun does not have a population of one as a dot is just a predecessor of the 5 cell p13 gun.

Oh yes, that's true. Playing around a bit more I found another setup that evolves into a period-5 gun:

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x = 1, y = 1, rule = B1e2i4awtec5ae/S01e3iy4awt5ay6c
o!

[HotWheels9232]

The gun is a true gun as opposed to pseudo gun, which has a period that is a multiple of the period of the output spaceship stream, like this one.
However, this gun does not have a population of one as a dot is just a predecessor of the 5 cell p13 gun.

Oh yes, that's true. Playing around a bit more I found another setup that evolves into a period-5 gun:

Code: Select all

x = 1, y = 1, rule = B1e2i4awtec5ae/S01e3iy4awt5ay6c
o!

I think it could be thought as a moving wick with vaccum as the endposts, because they are technically interacting like those ones:

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x = 31, y = 16, rule = B3-q4q/S23
12b2o15bo$13b2o14b2o$12bo15bobo$9b2o$10b2o13b3o$9bo17bo$6b2o18bo$7b2o
13b2o$6bo16b2o$3b2o17bo$4b2o13b2o$3bo14bobo$2o18bo$b2o13bo$o15b2o$15bo
bo!

My 2x3x5x17th post!