My apologize if a thread like this has already been created. I've been searching in the forum, and I didn't find one.
By talking about One Dimensional Celluar Automatas, I reduce the discussion to Life-Like Cellular Automatas only.
It's obvious that there aren't many options for different rules and patterns with a one-line limitation, but I still managed to get some interesting things.
There are overall 32 different rules for 1D, I think. Fix me if I'm wrong.
I allowed myself to put the rules in different categories-
Rules with L1 (every dead cell that has one neighbor turns alive) are called Expanders, because they always lead to infinite growth (not always infinite GROWTH, but infinite bounding box that expands quickly). It's pretty easy to prove- On the sides of the pattern's bounding box, there are always dead cells with exactly 1 living cell nearby.
L2- Fillers. Outside of the bounding box, there aren't any dead cells with two or more living cells nearby, so it can't help you with expanding. But, it fills a lot of cells inside the bounding box, and helps with filling in gaps.
L0- Unbounded. NOTE- This rule is only for theory. We can't really examine it, because every single pattern examined with that rule will lead to infinite population after the first generation. People might say it doesn't really count, so I'm only putting this in theory, and for now, we'll put it on the side.
Infertility- Rules that can't grow new life (I need help with the name of this rule). All of the patterns with this rule will either lead to a still life or will dissolve into nothing.
S1 (live cells with one neighbor keep surviving)- Even Rules. I called it like this, because then a basic still life of a pair of two cells, one next to each other, comes up.
S2- Crowded. Cells survive when in high population.
S0- Solitary. Cells survive when they have no living cells nearby.
Vanishing- Rules that can't let cells survive for more than one generation, like GoL's Pheonix patterns. This rule can lead to many interesting patterns, but not to Still Lives.
Any rule that has a few things combined will have mixed names. For an example, L2 S0+1 will be a filler, a solitary and an even pattern. Of course, you really don't have to follow the names, it's something that I thought of in 5 minutes in class. When talking about serious patterns, we can just use the codes.
Here are some things I managed to realise- I haven't put the proof in here, but they are really easy to proof;
1. Spaceships can't be exist at any combination of rules and patterns in 1D Life-Like Cellular Automata.
2. Still Lives, Oscillators and other patterns that can't grow without bound can't be Expanders or Unbounded.
3. Oscillators can't start or progress with a single point.
There is, though, a nice, small Oscillator in one of the rules.
Rule: L2S0+1 (Same rule I mentioned as an example)
O.O- Gen.1
OOO- Gen.2
O.O- Gen.3
Sorry for not making a real code to paste on Golly and other programs, I just wanted to expand more information about it.
So, post your discoveries about patterns in any of the 1D rules.
One Dimensional CA
Re: One Dimensional CA
Anyone..?
I have figured out four more things-
1. For infinite-growing patterns, the only possible growth rate is 2t (double linear). That's because patterns that expand to an infinite bounding box must be expanders (thus the name), and expanders always increase in both directions. So, a spread of 2 cells per second.
2. It is possible to create an agar if you use the fillers rule. Something like a dead-live-dead-live-dead row that lasts until infinity is, technicly, an agar with period 2.
3. It is possible to create a special kind of spaceship, but not purely. It needs the help of a big pattern from the sides to keep surviving, and for the spaceship to go an infinite distance, the supporting pattern needs to be an agar.
4. You can't build an Oscillator from two attached living cells. That means something important- The Oscillator I discovered (L2S0+1, O.O) Is proven to be the smallest both in terms of minimal population and bounding box.
I think it can help with the research.
I have figured out four more things-
1. For infinite-growing patterns, the only possible growth rate is 2t (double linear). That's because patterns that expand to an infinite bounding box must be expanders (thus the name), and expanders always increase in both directions. So, a spread of 2 cells per second.
2. It is possible to create an agar if you use the fillers rule. Something like a dead-live-dead-live-dead row that lasts until infinity is, technicly, an agar with period 2.
3. It is possible to create a special kind of spaceship, but not purely. It needs the help of a big pattern from the sides to keep surviving, and for the spaceship to go an infinite distance, the supporting pattern needs to be an agar.
4. You can't build an Oscillator from two attached living cells. That means something important- The Oscillator I discovered (L2S0+1, O.O) Is proven to be the smallest both in terms of minimal population and bounding box.
I think it can help with the research.
Just a 13-years old kid.