Multicolor Life variants
-
- Posts: 1175
- Joined: June 14th, 2014, 5:03 pm
- Contact:
Multicolor Life variants
People have made quite a few multicolor life variants, including Immigration and QuadLife. With the restrictions that live cells cannot change color and colors must be treated completely symmetrically, those and ordinary B3/S23 are the only possible variants. However, other variants should be possible if smaller symmetry groups are allowed. Which permutation groups can be realized with multicolor Life variants, and what interesting patterns exist in these?
-
- Posts: 5143
- Joined: August 31st, 2020, 5:58 pm
Re: Multicolor Life variants
I can think of at least one other such variant: There are two colors, and each newly-born cell takes the color that an odd number of live neighbors have. One interesting question concerning this rule is whether patterns in this rule would tend to eventually all become one color,fluffykitty wrote: ↑December 23rd, 2020, 6:37 pmWith the restrictions that live cells cannot change color and colors must be treated completely symmetrically, those and ordinary B3/S23 are the only possible variants.
I am tentatively considering myself back.
Re: Multicolor Life variants
I think (don't quote me on this) that the last possible variants for two-colour Life are "Even" and "Minority".MathAndCode wrote: ↑December 23rd, 2020, 7:03 pmI can think of at least one other such variant: There are two colors, and each newly-born cell takes the color that an odd number of live neighbors have. One interesting question concerning this rule is whether patterns in this rule would tend to eventually all become one color,
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
anythingsonata wrote:July 2nd, 2020, 8:33 pmconwaylife signatures are amazing[citation needed]
-
- Posts: 5143
- Joined: August 31st, 2020, 5:58 pm
Re: Multicolor Life variants
Here are the four distinct gliders in Minority besides color inversions.
The two gliders in the top row each have period four, and the two gliders in the bottom row each have period 28. All four gliders are glide-reflective, and none are their own color inversions.
Code: Select all
x = 13, y = 13, rule = Minority
.A9.A$2A8.2A$A.A7.A.B8$.A9.A$AB8.AB$A.A7.A.B!
I am tentatively considering myself back.
Re: Multicolor Life variants
FYI, I'm the creator of Minority, because I had this idea a few days ago. It was originally created as a more aggressive variant of Immigration (to prefer attacks), but the ash turned out to be stripy.
Two LWSSes I know of so far:
They have impressive periods.
I also created Infect to get rid of the "living cells must not change color" restriction.
Two LWSSes I know of so far:
Code: Select all
x = 5, y = 11, rule = Minority
A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!
I also created Infect to get rid of the "living cells must not change color" restriction.
-
- Posts: 5143
- Joined: August 31st, 2020, 5:58 pm
Re: Multicolor Life variants
In Minority, any two colorations of the same repeating pattern in ConwayLife can have their colorations XORed in all phases.Hunting wrote: ↑December 25th, 2020, 5:04 amTwo LWSSes I know of so far:
Code: Select all
x = 5, y = 11, rule = Minority A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!
Code: Select all
x = 12, y = 10, rule = Minority
A2BA$A3.B$B$.A2.B2.AB2A$7.A3.B$7.B$2ABA4.A2.B$A3.A$A$.A2.A!
I am tentatively considering myself back.
Re: Multicolor Life variants
You can also have variants in which, say, cells of a different color are born from three of the same color
not active here but active on discord
Re: Multicolor Life variants
Those being what I originally meant when I said Even and Minority, though I can't complain about the interpretation.
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
anythingsonata wrote:July 2nd, 2020, 8:33 pmconwaylife signatures are amazing[citation needed]
Re: Multicolor Life variants
MathAndCode wrote: ↑December 25th, 2020, 8:59 pmIn Minority, any two colorations of the same repeating pattern in ConwayLife can have their colorations XORed in all phases.Hunting wrote: ↑December 25th, 2020, 5:04 amTwo LWSSes I know of so far:
Code: Select all
x = 5, y = 11, rule = Minority A2BA$A3.B$B$.A2.B4$2ABA$A3.A$A$.A2.A!
Code: Select all
x = 12, y = 10, rule = Minority A2BA$A3.B$B$.A2.B2.AB2A$7.A3.B$7.B$2ABA4.A2.B$A3.A$A$.A2.A!
Code: Select all
x = 14, y = 14, rule = Minority
2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!
-
- Posts: 5143
- Joined: August 31st, 2020, 5:58 pm
Re: Multicolor Life variants
Hunting wrote: ↑December 29th, 2020, 8:18 amCode: Select all
x = 14, y = 14, rule = Minority 2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!
Code: Select all
x = 25, y = 29, rule = Minority
2A9.2A$A10.A$.A.A8.A.B2$3.A.A8.A.A2$5.A.B8.A.B2$7.A.A8.A.A2$9.A.A8.A.
B2$11.A.A8.A.A$12.2A9.2A2$5.2A$5.A$6.A.B2$8.A.A2$10.A.A2$12.A.A2$14.A
.B2$16.A.A$17.2A!
I am tentatively considering myself back.
- creeperman7002
- Posts: 301
- Joined: December 4th, 2018, 11:52 pm
Re: Multicolor Life variants
It appears that is an emulation of Rule 150.MathAndCode wrote: ↑December 29th, 2020, 2:23 pmHunting wrote: ↑December 29th, 2020, 8:18 amCode: Select all
x = 14, y = 14, rule = Minority 2A$A$.A.A2$3.A.A2$5.A.B2$7.A.A2$9.A.A2$11.A.A$12.2A!
Code: Select all
x = 25, y = 29, rule = Minority 2A9.2A$A10.A$.A.A8.A.B2$3.A.A8.A.A2$5.A.B8.A.B2$7.A.A8.A.A2$9.A.A8.A. B2$11.A.A8.A.A$12.2A9.2A2$5.2A$5.A$6.A.B2$8.A.A2$10.A.A2$12.A.A2$14.A .B2$16.A.A$17.2A!
B2n3-jn/S1c23-y is an interesting rule. It has a replicator, a fake glider, an OMOS and SMOS, a wide variety of oscillators, and some signals. Also this rule is omniperiodic.
viewtopic.php?f=11&t=4856
viewtopic.php?f=11&t=4856
Re: Multicolor Life variants
It just so happens I've just been studying these. Specifically, I've been looking at the possibilities for colourified CAs subject to these constraints:
- The underlying CA (colours flattened) is Life-like in the strictest sense - 2D square grid, two states, outer-totalistic, Moore neighbourhood.
- Surviving cells don't change colour.
- Colour-totalistic - colour of a born cell depends only on the bag of neighbour colours, not how they are arranged.
- Colour-symmetric - if the colours are permuted the CA behaves the same.
- Two live state colours: majority (Immigration), odd, even, minority
- Four live state colours: remaining colour for 3 different colours in neighbourhood (necessary for colour-symmetry); majority (QuadLife) or odd for 1 or 2 different colours in neighbourhood.
- There would need to be a unique third state for 3+3 to give birth to.
- Thus there are at least three states, thus must be a unique fourth state for 2+2+2 to give birth to.
- However, this fourth state means the aforementioned third state can't be unique.
- Entity Valkyrie 2
- Posts: 1758
- Joined: February 26th, 2019, 7:13 pm
- Contact:
Re: Multicolor Life variants
By the way, my rule EV2QuadColor is a marked version of QuadLife.
Bx222 IS MY WORST ENEMY.
Please click here for my own pages.
My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box
Please click here for my own pages.
My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box
Re: Multicolor Life variants
Is this something you've published somewhere? I can't seem to find it.Entity Valkyrie 2 wrote: ↑July 29th, 2021, 9:42 pmBy the way, my rule EV2QuadColor is a marked version of QuadLife.
BTW, I recently made a QuadLife rule file for Golly (as yet unpublished), intended for study purposes, with Unknown and Influence states. Unknown means a live cell whose colour is unknown. Influence is the same with the added rule that, when a cell is born, if Unknown and Influence are both in the neighbourhood that gave birth to it then the born cell is Influence; as such, it's good for seeing what future cells might possibly be influenced by the colour of a specific cell.