ConwayLife.com

Posted: **November 13th, 2021, 1:27 am**

I was preparing a new thread to gather theorems about existence of still lifes, oscillators, spaceships, expanding patterns, and vanishing patterns in OT and INT rules, and speed limits for moving patterns. Which preexisting results should I present in the OP, and how should I present them? In particular, should I present any proofs or links to proofs?

Posted: **November 29th, 2021, 11:05 pm**

otismo wrote: November 29th, 2021, 8:47 pmMaybe someone could explain how it does that.

It's basically just random chance. The forward movement mechanism is destroyed because it tries to go in two directions at once, and the resulting junk just happens to form a new forward movement mechanism before it can die completely. This sort of behavior is fairly common; here's a similar example in an outer-totalistic rule.

Code: Select all

x = 5, y = 6, rule = B01245/S01245
b3o$obobo$5o$5o$b2obo$2bo!

Posted: **December 15th, 2021, 6:59 pm**

Is it possible for any rules to non-trivially support C4_2 or D4_x2 symmetry, like how D8_2 can be supported?

Given how Catagolue generates the _1 versions of these soups, I'm not at all hopeful.

Code: Select all

x = 107, y = 32, rule = B3/S23
76b3ob2ob2o2bobob4o5bo3bo$b3ob2ob2o2bob5o5bo3bo49b2o2bo2bob2obo2b4obo
2bob2obo$3b2o2bo2bob2obob4obo2bob2obo44b4obob5obobo3b6o4bobo$4obob5obo
bo2b6o4bobo45bob2o2bo2b2o2bo4bo2b4o2b4o$bob2o2bo2b2o2bo3bo2b4o2b4o50bo
2bo2b3ob6o4bobobo$6bo2bo2b9o4bobobo46bo2b4ob2o4bobo3b3o2bo2bobo$bo2b4o
b2o4b2o3b3o2bo2bobo44bo2bo2bob2obob2obo6bob3o3bo$o2bo2bob2obob3o6bob3o
3bo46b2o3b3o4b3obo2b4obob3o$2b2o3b3o4b2obo2b4obob3o46b3ob3o2bo3bo2bob
3o2b2o3bobo$b3ob3o2bo3bobob3o2b2o3bobo46b2obobob6obo2b2obob4obobo$2b2o
bobob7o2b2obob4obobo45b2ob2ob2obobob3o3b4o2bob3o$b2ob2ob2obobob2o3b4o
2bob3o20b4o22b2obo3b3obo4b2o3bo2bo2b2o$b2obo3b3obo3b2o3bo2bo2b2o18b3o
3b2o20b5o3b2o7b2ob3o4bo2b2o$5o3b2o6b2ob3o4bo2b2o15b2o6bo20b2o2bo2bo3b
3ob2obo3bo2bobob2o$2o2bo2bo3b3obobo3bo2bobob2o16bo7bo20bo3b2o2bo2b2o2b
o5b5ob2o2bo$o3b2o2bo2b2o2bo4b5ob2o2bo15bo5b2o21bo3bob2ob2o2bo3b2o2bo2b
obo2b2o$3ob4ob2o2b2ob2o2b2ob4ob3o21bo23b2o2bobo2bo2b2o3bo2b2ob2obo3bo$
o2b2ob5o4bo2b2o2bo2b2o3bo21b2o21bo2b2ob5o5bo2b2o2bo2b2o3bo$b2obobo2bo
3bobob3o3bo2bo2b2o22bo22b2obobo2bo3bob2ob3o3bo2bo2b2o$2o2bo4b3ob2o6b2o
3b5o44b2o2bo4b3ob2o7b2o3b5o$2b2o2bo2bo3b2o3bob3o3bob2o47b2o2bo2bo3b2o
4bob3o3bob2o$b3obo2b4o3b2obobob2ob2ob2o46b3obo2b4o3b3obobob2ob2ob2o$ob
ob4obob2o2b7obobob2o46bobob4obob2o2bob6obobob2o$obo3b2o2b3obobo3bo2b3o
b3o24bo20bobo3b2o2b3obo2bo3bo2b3ob3o$b3obob4o2bob2o4b3o3b2o47b3obob4o
2bob3o4b3o3b2o$o3b3obo6b3obob2obo2bo2bo44bo3b3obo6bob2obob2obo2bo2bo$o
bo2bo2b3o3b2o4b2ob4o2bo45bobo2bo2b3o3bobo4b2ob4o2bo$bobobo4b9o2bo2bo
51bobobo4b6ob3o2bo2bo$4o2b4o2bo3bo2b2o2bo2b2obo45b4o2b4o2bo4bo2b2o2bo
2b2obo$obo4b6o2bobob5obob4o44bobo4b6o3bobob5obob4o$ob2obo2bob4obob2obo
2bo2b2o47bob2obo2bob4o2bob2obo2bo2b2o$2bo3bo5b5obo2b2ob2ob3o47bo3bo5b
4obobo2b2ob2ob3o!

Code: Select all

x = 122, y = 32, rule = B3/S23
92bo3bo5b4obobo2b2ob2ob3o$2bo3bo5b5obo2b2ob2ob3o62b2obo2bob4o2bob2obo
2bo2b2o2bo$2b2obo2bob4obob2obo2bo2b2o2bo59b3o4b6o3bobob5obob2obo$3o4b
6o2bobob5obob2obo60bobo2b4o2bo4bo2b2o2bo2b5o$bobo2b4o2bo3bo2b2o2bo2b5o
64bo4b6ob3o2bo2bo2bobo$5bo4b9o2bo2bo2bobo61bo2b2o2b3o3bobo4b2ob3o2bobo
$bo2b2o2b3o3b2o4b2ob3o2bobo59bo2bo2bobo6bob2obob2ob3o3bo$o2bo2bobo6b3o
bob2ob3o3bo61b2o3b4o2bob3o4b3obob3o$2b2o3b4o2bob2o4b3obob3o61b3ob3o2b
3obo2bo3bo2b2o3bobo$b3ob3o2b3obobo3bo2b2o3bobo61b2obobobob2o2bob6ob4ob
obo$2b2obobobob2o2b7ob4obobo26b5o29b2ob2ob2ob2o3b3obob3o2bob3o$b2ob2ob
2ob2o3b2obob3o2bob3o27bo3bo29b2obo3b3o2b2o4bo2bo2bo2b2o$b2obo3b3o2b2o
3bo2bo2bo2b2o27bo3bo29b5o3b2o3b2o5b3o4bo2b2o$5o3b2o3b2o4b3o4bo2b2o28bo
30b2o2bo2bo3b3ob2obo3bo2bobob2o$2o2bo2bo3b3obobo3bo2bobob2o29bo30bo3b
2o2bo2b2o3bo4b5ob2o2bo$o3b2o2bo2b2o2bo4b5ob2o2bo28bo30bo3bob2ob2o2bo3b
2o2bo2bobo2b2o$3ob4ob2o2b2ob2o2b2ob4ob3o28bo31b2o2bobo2bo2b2o3bo2b2ob
2obo3bo$o2b2ob5o4bo2b2o2bo2b2o3bo27bo31bo2b2ob5o4bo3b2o2bo2b2o3bo$b2ob
obo2bo3bobob3o3bo2bo2b2o60b2obobo2bo3bob2ob3o3bo2bo2b2o$2o2bo4b3o4b2o
3b2o3b5o59b2o2bo4b3o5b2o3b2o3b5o$2b2o2bo2bo2bo3b2o2b3o3bob2o62b2o2bo2b
o2bo4b2o2b3o3bob2o$b3obo2b3obob2o3b2ob2ob2ob2o61b3obo2b3obob3o3b2ob2ob
2ob2o$obob4ob7o2b2obobobob2o30bo30bobob4ob6obo2b2obobobob2o$obo3b2o2bo
3bobob3o2b3ob3o60bobo3b2o2bo3bo2bob3o2b3ob3o$b3obob3o4b2obo2b4o3b2o62b
3obob3o4b3obo2b4o3b2o$o3b3ob2obob3o6bobo2bo2bo59bo3b3ob2obob2obo6bobo
2bo2bo$obo2b3ob2o4b2o3b3o2b2o2bo60bobo2b3ob2o4bobo3b3o2b2o2bo$bobo2bo
2bo2b9o4bo65bobo2bo2bo2b3ob6o4bo$5o2bo2b2o2bo3bo2b4o2bobo60b5o2bo2b2o
2bo4bo2b4o2bobo$ob2obob5obobo2b6o4b3o59bob2obob5obobo3b6o4b3o$o2b2o2bo
2bob2obob4obo2bob2o61bo2b2o2bo2bob2obo2b4obo2bob2o$b3ob2ob2o2bob5o5bo
3bo62b3ob2ob2o2bobob4o5bo3bo!

Posted: **December 31st, 2021, 1:34 am**

What are the Langton’s Ant(s) rules?
I only know that it’s a rule, but have no idea what rule does it follows.
Can anyone explain that to me, please?

Posted: **December 31st, 2021, 10:26 am**

Ohhhhhhhhh wrote: December 31st, 2021, 1:34 am What are the Langton’s Ant(s) rules?
I only know that it’s a rule, but have no idea what rule does it follows.
Can anyone explain that to me, please?

Wikipedia has a nice set of explanations for the original Langton's Ant and extended variations.

Langtons Ant sits on grid of white and black cells. If it is on a white cell it turns right and moves forward, and if it is on a black cell it turns left and moves forward. Every time it leaves a cell, it changes the color to the other one.

One can extend this by adding more states, which change in a cycle like generations rules. For example if you had white, black, red.

If on white, turn right, set cell color to black, and move forward

If on black, turn left, set cell color to red, and move forward

If on red, turn right, set cell color to white, and move forward

You can have any number of states and write how it turn using "L" for left turn and "R" for right turn.
Langton's Ant is "RL" and the example above is "RLR"

Posted: **January 4th, 2022, 3:41 pm**

What are the restrictions in a rulestring for an isotropic non-totalistic rule that can be lifelike? The reason I ask is because I'm working on a program that randomly generates possible rulestrings and want to optimize it. For example, It already doesn't generate rules with B1 and B2a . Sorry for the confusing question.

Posted: **January 4th, 2022, 3:48 pm**

NimbleRogue wrote: January 4th, 2022, 3:41 pm What are the restrictions in a rulestring for an isotropic non-totalistic rule that can be lifelike? The reason I ask is because I'm working on a program that randomly generates possible rulestrings and want to optimize it. For example, It already doesn't generate rules with B1 and B2a . Sorry for the confusing question.

Lifelike by definition means it's outer-totalistic. It has nothing to do with how similar it is to Life visually.

Posted: **January 4th, 2022, 4:39 pm**

I meant to say "a rule that's able to support spaceships oscillators/still lifes, etc" as opposed to "lifelike".

Posted: **January 4th, 2022, 7:32 pm**

If you want ships, B2e or B3a is required to expand diagonally, and B2c or B3i is required to expand orthogonally.

As you said B12a is generally avoided, as is B0 for the complexity that comes with it.

Everything else is optional, which is part of why the INT rulespace is so large. I can recommend EnumPattEvo as a good tool for finding rules with interesting objects.

Posted: **January 5th, 2022, 12:51 am**

NimbleRogue wrote: January 4th, 2022, 4:39 pm I meant to say "a rule that's able to support spaceships oscillators/still lifes, etc" as opposed to "lifelike".

Then LFoD would pass.

Code: Select all

x = 11, y = 2, rule = B2/S0
o2bo4b2o$4bo2bo2bo!

Posted: **January 26th, 2022, 10:56 am**

Code: Select all

x = 1, y = 1, rule = MAPgirA+AASJAAAQgAACQAAAAEAAACAAAEACAAEAAqAAAAAAAAAEAAAAAwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

How does MAP work?

Posted: **January 26th, 2022, 6:57 pm**

How do I make the colors different?
I want it so that I can make an instance of TripleLife have, instead of
0 black
a green
b red
c blue
ab yellow
and so on,
have
0 white
a no green (purple)
b no red (cyan)
c no blue (yellow)
ab no green or red (blue)
and so on for the states.

Posted: **January 26th, 2022, 7:49 pm**

In Golly, press the B key; this will invert all the colors on the grid. I don't know if it's possible in LifeViewer.

Posted: **January 26th, 2022, 8:37 pm**

breaker's glider gun wrote: January 26th, 2022, 6:57 pm How do I make the colors different?
...

An alternative is to go to the layer menu, and then pick "Set Layer Colors" click this, and edit each of the colors. Hope this helped

Posted: **January 26th, 2022, 8:39 pm**

Wyirm wrote: January 26th, 2022, 8:37 pm
breaker's glider gun wrote: January 26th, 2022, 6:57 pm How do I make the colors different?
...
An alternative is to go to the layer menu, and then pick "Set Layer Colors" click this, and edit each of the colors. Hope this helped

??
what layer menu?
what is "this" that I click?

Posted: **January 26th, 2022, 9:10 pm**

At the top of the screen

breaker's glider gun wrote: January 26th, 2022, 8:39 pm
Wyirm wrote: January 26th, 2022, 8:37 pm
breaker's glider gun wrote: January 26th, 2022, 6:57 pm How do I make the colors different?
...
An alternative is to go to the layer menu, and then pick "Set Layer Colors" click this, and edit each of the colors. Hope this helped
??
what layer menu?
what is "this" that I click?

At the top of the golly window there should be 6 tabs, layer is the 5th tab.

Posted: **January 27th, 2022, 1:12 am**

Wyirm wrote: January 26th, 2022, 10:56 am
Code: Select all
x = 1, y = 1, rule = MAPgirA+AASJAAAQgAACQAAAAEAAACAAAEACAAEAAqAAAAAAAAAEAAAAAwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!
How does MAP work?

Take a look at the explanation on this page
http://golly.sourceforge.net/Help/Algor ... kLife.html
While we're here, I'd like to say that I think there should be a more intuitive MAP notation. The current one is kind of tedious to create, and hard to understand what a rule will be like from its rulestring. I think a more intuitive one, like this would be easier to use, manipulate, and interpret.

Posted: **February 2nd, 2022, 4:48 pm**

in what isotropic non-totalistic rules does the U-turner exibits some kind of interesting behavior?

Posted: **February 4th, 2022, 5:13 am**

C28 wrote: February 2nd, 2022, 4:48 pm in what isotropic non-totalistic rules does the U-turner exibits some kind of interesting behavior?

That's up for you to determine. But here's a rule where it is a p236 oscillator:

Code: Select all

x = 4, y = 4, rule = B2n34ez5ek/S23-ceky6en
b3o$b3o$obo$2o!

Posted: **February 4th, 2022, 10:01 am**

LaundryPizza03 wrote: February 4th, 2022, 5:13 am
C28 wrote: February 2nd, 2022, 4:48 pm in what isotropic non-totalistic rules does the U-turner exibits some kind of interesting behavior?
That's up for you to determine. But here's a rule where it is a p236 oscillator:
Code: Select all
x = 4, y = 4, rule = B2n34ez5ek/S23-ceky6en
b3o$b3o$obo$2o!

i wonder if that can be made into a gun

Posted: **February 6th, 2022, 4:03 am**

Is there an INT rule where all oscillators with period n with the smallest number of cells exist, assuming that n is an arbitrary natural number?

Posted: **February 7th, 2022, 9:10 pm**

In range-1 isotropic non-totalistic rules, is it at all possible to prove that a given spaceship speed can be constructed using an adjustable-speed spaceship but cannot otherwise arise naturally as a non-adjustable spaceship speed?

Posted: **February 10th, 2022, 12:18 pm**

the other day i was trying to set up a HROT rule using the NW thing to make my own weighted neighborhood, but i kept running into a problem. whenever i used the numbers 7, 8, or 9 in it, it wouldn't work correctly, instead having those neighbors valued at completely different weights (i could figure out what weights they were being valued as, just that they weren't anything from 6 to 10), and when i checked on the page in conwaylife wiki, it doesn't even mention them. what do 7, 8, 9 do if they aren't valued as cells with those weights, and why?

edit: i checked and when doing the 100 digit version of the notation, 10, 11, 12, etc also don't seem to do what would be expected. could someone please explain whatever is going on?

Posted: **February 23rd, 2022, 7:18 pm**

Is this a shuttle, a hassler, or just an oscillator?

Code: Select all

x = 4, y = 19, rule = B3aeij4aejrw/S23
bo$obo$obo$bo5$b3o$3bo$b3o5$bo$obo$obo$bo!

Posted: **February 23rd, 2022, 7:30 pm**

Herschel of Ostropol wrote: February 23rd, 2022, 7:18 pm Is this a shuttle, a hassler, or just an oscillator?
Code: Select all
x = 4, y = 19, rule = B3aeij4aejrw/S23
bo$obo$obo$bo5$b3o$3bo$b3o5$bo$obo$obo$bo!

although this belongs in another thread, this is a good question

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