## Plus-Minus (+/-) Rules

For discussion of other cellular automata.
ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Plus-Minus (+/-) Rules

Hi!

I've implemented a new way to define generations-like rules. Maybe someone has done this before, I don't know. Anyway, it creates rules with interesting behaviors.

How it works

This rules use the sum of the values of its neighbors. For example, in a +4 rule, every cell whose neighbors add to 4 will increment its value by 1 in the next generation:

Code: Select all

``````101     200     100
1X0     2X0     0X0
010     000     102
``````
Rules are defined using the format +X-Y:Z (i.e: +5-4-6:3, +6+12-5:4), where +X means the number that neighbors need to add to for a cell to increment its value, -Y means the number that neighbors need to add to for a cell to NOT decrement its value, and :Z is the number of generations (allowed "values"). When saving the rule to a file, the ":" symbol is not allowed, so I use "c" (i.e. +4-5-6c3.tree)

How to create new rules

To create rules, you need the make-ruletree.py Golly script (from here: http://ruletablerepository.googlecode.c ... uletree.py )

Then, copy the following script to your clipboard (modify name, n_states, states, plus and minus to match your desired rule) and run make-ruletree.py from Golly:

Code: Select all

``````name = "+4-5-6c3"
n_states = 3 # must match states
n_neighbors = 8
def transition_function(a):
# +4-5-6:3
plus = [4] # +x
minus = [5,6] # -x
states = 3 # must match n_states

p = 0
m = 0
n = a[0] + a[1] + a[2] + a[3] + a[4] + a[5] + a[6] + a[7]
for i in plus:
if n == i:
p = 1
for i in minus:
if n == i:
m = 1
if p == 1:
if a[8] == (states - 1):
return a[8]
else:
return a[8] + 1
if m == 0:
if a[8] == 0:
return a[8]
else:
return a[8] - 1
return a[8]
``````
It will generate a RuleTree. Hope it's not too complex, I can't think of a way to simplify it any further.

Interesting rules

+4-5-6:3 (+4-5-6c3.tree -> http://tinypaste.com/5bca2 )

This rule shows Life-like behavior. Tends to expand infinitely, but only because of a very common puffer that appears often; without that puffer, it settles down. Has a lot of different still life, oscillators and spaceships. Lines of width 1 act as "walls"

+4-6-7-8-9-10:4 (+4-6-7-8-9-10c4.tree -> http://tinypaste.com/499d8d )

This rule has a lot of different and complex still lifes, yet it stabilizes quickly. It also has a surprisingly slow and complex spaceship that appears from a really simple pattern:

Code: Select all

``````x = 2, y = 3, rule = +4-6-7-8-9-10c4
C\$CA\$.C!
``````
And... that's it. If you're interested in any of this or other rules, consider creating another thread (I was going to create one for +4-5-6:3, but I don't want to flood the forum)

Ask me anything!

Keiji
Posts: 58
Joined: May 11th, 2010, 5:32 pm

### Re: Plus-Minus (+/-) Rules

I've been playing around with +4-5-6:3 - it's not quite as Life-like as I'd hope:

- So far, I've found oscillators only with periods 1, 2, 5, 57 and 79.

- Almost anything that has single diagonal symmetry tends to become a chaotic (albeit symmetrical) mess and emit spaceships, puffers, and rakes as long as I dare to run it. Almost anything that doesn't have that type of symmetry tends to be a methuselah which stabilizes within 2,500 generations to the empty universe, or if I'm lucky, some very simple period 2 oscillators.

- I've found exactly one spaceship, one puffer and one rake so far, which are all pretty much related to each other and the chaotic messes generate these (and no other forms of spaceships/puffers/rakes).

- All the quadruplets, pentominoes and hexominoes (with all their cells in state 2) fall into the "almost anything" categories above - they either exhibit infinite growth or they stabilize without emitting any moving objects.

- All the spaceship collisions I've tried become the same kind of patterns again (though one possible collision deletes one of the spaceships while the other continues undisturbed).

From what I've seen so far, I would bet that it's impossible to build a Turing machine in this automaton...

If you've managed to find a period 3 oscillator, diagonal spaceship, shuttle, gun, reflector or something else interesting like that I'd be interested to hear about it. I might try messing with related rules later though.

Edit: Here's an archive of all the stuff I've found so far.

This is why signature character limits are pointless.

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: Plus-Minus (+/-) Rules

Some period 3 oscillators:

Code: Select all

``````x = 51, y = 6, rule = +4-5-6c3
22.B2.B12.A3.B2.B3.A\$2.B4.B13.2B2.2B11.A4B2.4BA\$AB.B2.B.BA27.A12.A\$AB
.B2.B.BA28.A4B2.4BA\$2.B4.B13.2B2.2B11.A3.B2.B3.A\$22.B2.B!
``````
A period 84 oscillator:

Code: Select all

``````x = 15, y = 15, rule = +4-5-6c3
4.B5.B\$3.2B5.2B\$2.A3.3A3.A\$.B.2B5.2B.B\$2B.B7.B.2B2\$2.A9.A\$2.A9.A\$2.A
9.A2\$2B.B7.B.2B\$.B.2B5.2B.B\$2.A3.3A3.A\$3.2B5.2B\$4.B5.B!
``````
A p36 oscillator in a box:

Code: Select all

``````x = 23, y = 23, rule = +4-5-6c3
4.BA2.B5.B2.AB\$3.2BA2.2B3.2B2.A2B\$2.A17.A\$.B.17B.B\$2B.B15.B.2B\$2A.B
15.B.2A\$3.B15.B\$3.B15.B\$2B.B6.3A6.B.2B\$.B.B6.BAB6.B.B\$3.B4.AB3.BA4.B\$
3.B4.2A.A.2A4.B\$3.B4.AB3.BA4.B\$.B.B6.BAB6.B.B\$2B.B6.3A6.B.2B\$3.B15.B\$
3.B15.B\$2A.B15.B.2A\$2B.B15.B.2B\$.B.17B.B\$2.A17.A\$3.2BA2.2B3.2B2.A2B\$
4.BA2.B5.B2.AB!
``````
Some spaceships (there are at least three different types of spaceships; haven't found diagonal ones, though):

Code: Select all

``````x = 17, y = 333, rule = +4-5-6c3
2\$2.2A.A\$2.2B.A\$2.2AB21\$3.AB.A\$2.AB2A\$2.A6.A\$3.6BA\$3.2A4.A8\$3.AB\$2.AB
A\$2.A6.A\$3.6BA\$3.2A4.A14\$2.2AB\$2.2BAB\$2.A\$2.A3B\$3.A\$5.3B\$5.2A4\$2.2AB\$
2.2BAB\$2.A\$2.A3B\$3.A4.A\$5.3BA\$5.2A.A6\$2.2AB\$2.2BAB\$2.A6.A\$2.A6BA\$3.A
5.A\$5.2BA\$5.2A5\$2.2AB\$2.2BAB\$2.A6.A\$2.A6BA\$3.A5.A\$5.4BA\$5.2A2.A23\$4.A
\$3.A2BA\$2.A6.A\$2.7BA\$2.A6.A\$3.A2BA\$4.A5\$4.A4.A\$3.A5BA\$2.A6.A\$2.3B\$2.A
\$3.A2BA\$4.A4\$4.A4.A\$3.A5BA\$2.A6.A\$2.4B\$2.A6.A\$3.A5BA\$4.A4.A5\$4.A\$3.A
2BA\$2.A6.A\$2.7BA\$2.A6.A\$3.A5BA\$4.A4.A6\$4.A2.BA\$3.A4BA\$2.A7.A\$2.8BA\$2.
A7.A\$3.A4BA\$4.A2.BA7\$4.A\$3.A2BA\$2.A\$2.3B\$2.A\$3.A2BA\$4.A21\$5.AB\$4.AB2A
\$4.A\$5.2B\$4.A\$4.AB2A\$5.AB18\$5.AB\$4.AB2A\$4.A\$5.9B\$4.A\$4.ABA\$5.A.B\$6.2A
6\$5.A\$4.ABAB\$4.A3.A\$5.2B\$4.A\$4.AB2A\$5.AB6\$5.AB\$4.AB2A\$4.A3.A\$5.2B\$4.A
3.A\$4.AB2A\$5.AB6\$4.2A\$4.2BA\$4.A6.A\$4.A6BA\$4.A6.A\$4.2BA\$4.2A9\$10.A\$7.
2ABAB\$5.AB.B2.B\$4.ABA.B.B\$4.A3.A\$5.2B\$4.A\$4.AB2A\$5.AB17\$7.A\$6.A2BA\$4.
2A\$4.3BA\$3.A\$2.A2BA\$3.A\$4.3BA\$4.2A\$6.A2BA\$7.A5\$7.A2.A\$6.A4B\$4.2A6.BA\$
4.9BA\$3.A\$2.A13B\$3.A\$4.9BA\$4.2A6.BA\$6.A4B\$7.A2.A!

``````
And... I think that's it. I also have a collection of symmetrical still lifes, but haven't managed to do something interesting with them.

Keiji
Posts: 58
Joined: May 11th, 2010, 5:32 pm

### Re: Plus-Minus (+/-) Rules

Some nice stuff there.

Have you ever found those objects being generated by other patterns or were they all found specifically by themselves? (excluding the spaceship and wickstretcher that we've seen a thousand times, that is)

This is why signature character limits are pointless.

Keiji
Posts: 58
Joined: May 11th, 2010, 5:32 pm

### Re: Plus-Minus (+/-) Rules

I've been investigating +4-6-7-8-9-10c4. So far, I have only found that spaceship you already mentioned and oscillators of periods 2, 3, 4, 5, 6, 8, 9, 12, 14, 15, 17, 18, 21, 22, 24, 25, 26 and 42. Any luck finding anything more exotic or any indications of the possibility of universal constructors in this or a similar rule?

This is why signature character limits are pointless.