## Phoenices

For discussion of other cellular automata.
Ntsimp
Posts: 46
Joined: June 8th, 2010, 9:11 am

### Phoenices

Just to keep things simple, let's say a "phoenix" is an oscillator in which no cells ever survive.
In which rules can they exist, and which periods can they have?
Since removing survival rules can never affect a phoenix, finding phoenices is equivalent to finding oscillators in rules without survival.
The LifeWiki article claims a proof has been found that no phoenix in Conway's Game of Life (so in B3/S) can have period 3.
In fact, all the phoenices I can find in any rules have even periods. I've found periods 2, 4, 6, 8, 10, and 14 so far.
I've found phoenices whose simplest rules are B2/S, B24/S, B25/S, B3/S, B34/S, B346/S, B35/S, and B36/S.

Then there's the rule B345/S. There are many oscillators in this rule, including periods 18, 22, 24, 26, 30, 32, 34, 38, 40, 42, 62, 66, 72,

velcrorex
Posts: 339
Joined: November 1st, 2009, 1:33 pm

### Re: Phoenices

There are p3 oscillators in B2/S, and likely other similar rules. They're much bigger than the smallest p2 or p4 oscillators. I think they're rarer because each phase must not share any cells with the other two phases.

Here's a few from my own collection. There's probably some slightly smaller examples around.

Code: Select all

``````x = 142, y = 118, rule = /2
31\$26bo50bo\$24boo6bo9bo18bo9bo6boo\$22bobo10bo4bo22bo4bo10bobo\$22boboo
4boo5bobbo9bobbo9bobbo5boo4boobo\$21bo6bo8bo5bo16bo5bo8bo6bo\$25bobo12b
oo3bobbo6bobbo3boo12bobo\$26b3ob7obbo3bo7boo7bo3bobb7ob3o\$22bo5bobbo7bo
7bo8bo7bo7bobbo5bo\$23bob3o7bo4bo9bobbo9bo4bo7b3obo\$23bobbo4bo3bo15boo
15bo3bo4bobbo\$26bo3boobo4bo3bo5bo6bo5bo3bo4boboo3bo\$26booboo7bo5b3o10b
3o5bo7booboo\$26bo3boobo4bo3bo5bo6bo5bo3bo4boboo3bo\$23bobbo4bo3bo15boo
15bo3bo4bobbo\$23bob3o7bo4bo9bobbo9bo4bo7b3obo\$22bo5bobbo7bo7bo8bo7bo7b
obbo5bo\$26b3ob7obbo3bo7boo7bo3bobb7ob3o\$25bobo12boo3bobbo6bobbo3boo12b
obo23bo\$21bo6bo8bo5bo16bo5bo8bo6bo15bo4boo\$22boboo4boo5bobbo9bobbo9bo
bbo5boo4boobo14boo\$22bobo10bo4bo22bo4bo10bobo21boobo\$24boo6bo9bo18bo9b
o6boo15b3o4b3obo\$26bo50bo17bo5bobo3bo\$94bobbobobbo\$99bo\$100boo\$106bo\$
93bobbo4bobobo\$91bobobbobo4bobo\$82bo4bo5b4o5boo\$43bo27bo6bo4boo7boobb
oo3bo\$38bobbo26bo3boobboo7boo4bo6bo\$40boobo22boo5b4o5bo4bo\$38bo3bo21bo
bo4bobobbobo\$34bobobbo24bobobo4bobbo\$43bobo4bo12bo\$35b3obo28boo\$48boo
20bo\$34b4obboo4bo20bobbobobbo\$33bobbo8bo16bo3bobo5bo\$45b3o15bob3o4b3o\$
36bo4bo6bo14boboo36bo6bo\$33b4o35boo19bo6bo3boobboo3bo\$32b3oboobboo4bob
o16boo4bo18bo3boobboo5b4o5boo\$32bo3boobbo3bo22bo20boo5b4o4bobobbobo4bo
bo\$32bo3boobbo3bo41bobo4bobobbobo4bobbo4bobobo\$32b3oboobboo4bobo37bobo
bo4bobbo19bo\$33b4o48bo26boo\$36bo4bo6bo41boo19bo\$45b3o44bo13bobbobobbo\$
33bobbo8bo43bobbobobbo9bo5bobo3bo\$34b4obboo4bo37bo3bobo5bo10b3o4b3obo\$
48boo35bob3o4b3o18boobo\$35b3obo45boboo19boo\$43bobo4bo43boo14bo4boo\$34b
obobbo47boo4bo20bo\$38bo3bo46bo\$40boobo\$38bobbo\$43bo!
``````
-Josh Ball.

velcrorex
Posts: 339
Joined: November 1st, 2009, 1:33 pm

### Re: Phoenices

This p3 works in B2 through B25678

Code: Select all

``````x = 91, y = 97, rule = /25678
30\$28bo\$30bo4bo\$24bo5bobbo\$33bo5bo\$25boo\$27bo9boo\$20bo6bo8bo\$22bo6bo6b
o6bo\$22bo11bo6bo\$23boo16bo\$18bo20boo\$25bo19bo\$19boo17bo\$43boo\$\$20boo\$
26bo17boo\$19bo19bo\$24boo20bo\$23bo16boo\$23bo6bo11bo\$21bo6bo6bo6bo\$28bo
8bo6bo\$26boo9bo\$38boo\$25bo5bo\$31bobbo5bo\$29bo4bo\$36bo!
``````
-Josh Ball.

Lewis
Posts: 320
Joined: March 17th, 2009, 5:26 pm
Location: UK
Contact:

### Re: Phoenices

I know this is slightly off-topic, but does the 12-cell phoenix in Life ever occur naturally? I've never checked all the way through Andrzej Okrasinski's census, but I expect that it shouldn't be too rare due to it's size and symmetry.

Paul Tooke
Posts: 111
Joined: May 19th, 2010, 7:35 am
Location: Cambridge, UK

### Re: Phoenices

Lewis wrote:
I know this is slightly off-topic, but does the 12-cell phoenix in Life ever occur naturally?
FWIW, I've been testing modifications to my random soup/agar program and it has turned up twice in test runs in Life. It may have shown up in others but I wasn't specifically looking for it. Furthermore, my progam only outputs one copy of anything that it sees, so I have no idea how frequently this pattern appears. Whether the patterns appearance in this context qualifies as 'occuring naturally' depends on your definition of 'natural'. Soups in symmetrical bounded universes yeild symmetrical patterns that may have little chance of appearing in an asymmetrical soup in an unbounded universe. The latter being closer to my interpretation of 'natural'.

checkman
Posts: 12
Joined: February 25th, 2014, 5:33 pm
Location: Tempe, AZ (Not Phoenix, Bob Schieffer!)
Contact:

### Re: Phoenices

Ntsimp wrote:Just to keep things simple, let's say a "phoenix" is an oscillator in which no cells ever survive.
In which rules can they exist, and which periods can they have?
Are there any Life-like CAs where you'd like this question answered in particular, for period 2?
Then there's the rule B345/S. There are many oscillators in this rule, including periods 18, 22, 24, 26, 30, 32, 34, 38, 40, 42, 62, 66, 72,
And the simplest phoenix with period 2 in B345/S appears to be one of width 3:

Code: Select all

``````x = 3, y = 6, rule = B345/S
3o2\$bo\$bo2\$3o!
``````

checkman
Posts: 12
Joined: February 25th, 2014, 5:33 pm
Location: Tempe, AZ (Not Phoenix, Bob Schieffer!)
Contact:

### Re: Phoenices

B34/S03456 has no phoenixes with period = 3.

See viewtopic.php?f=11&t=1323#p11194

Hunting
Posts: 1117
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Phoenices

Ntsimp wrote: The LifeWiki article claims a proof has been found that no phoenix in Conway's Game of Life (so in B3/S) can have period 3.
Sorry for extremenecroposting, but it is wrong. Removing S23 can't affect a phoneix, but it can affect those not-a-phoneix oscillators, and even unstable objects.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:

Code: Select all

``````#C Favorite Gun. Found by me.
x = 4, y = 6, rule = B2e3i4at/S1c23cijn4a
o2bo\$4o3\$4o\$o2bo!``````

testitemqlstudop
Posts: 1184
Joined: July 21st, 2016, 11:45 am
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Contact:

### Re: Phoenices

If a p3 phoenix exists in B3/S, then duh it exists in B3/S23!

Hunting
Posts: 1117
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Phoenices

testitemqlstudop wrote:If a p3 phoenix exists in B3/S, then duh it exists in B3/S23!
No, that's wrong. The p3 phoenix can has some cells which has 2 or 3 neighbours, when run in B3/S23 they will fail.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:

Code: Select all

``````#C Favorite Gun. Found by me.
x = 4, y = 6, rule = B2e3i4at/S1c23cijn4a
o2bo\$4o3\$4o\$o2bo!``````

testitemqlstudop
Posts: 1184
Joined: July 21st, 2016, 11:45 am
Location: in catagolue
Contact:

### Re: Phoenices

Whoops. I mean to say its converse:

If a p3 phoenix does NOT exist in B3/S, then a p3 phoenix cannot exist in B3/S23.

Hunting
Posts: 1117
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Phoenices

testitemqlstudop wrote:Whoops. I mean to say its converse:

If a p3 phoenix does NOT exist in B3/S, then a p3 phoenix cannot exist in B3/S23.
That's right, but it does not contradicts my sentence.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:

Code: Select all

``````#C Favorite Gun. Found by me.
x = 4, y = 6, rule = B2e3i4at/S1c23cijn4a
o2bo\$4o3\$4o\$o2bo!``````

PkmnQ
Posts: 666
Joined: September 24th, 2018, 6:35 am
Location: Server antipode

### Re: Phoenices

Hunting wrote:
testitemqlstudop wrote:Whoops. I mean to say its converse:

If a p3 phoenix does NOT exist in B3/S, then a p3 phoenix cannot exist in B3/S23.
That's right, but it does not contradicts my sentence.
In fact, using first-order logic, I can prove that one leads to the other.
A implies B, original statement.
Goal: Not B implies Not A.

A implies B.
I will assume Not B.
I will assume A.
I will deduce B from A implies B and A, using Modus Ponens (given).
I will deduce Not A from B and Not B, using Reductio Ad Absurdum (which i can break down, but it would be too long here)
I will deduce Not B implies Not A, using Deduction Theorem (given).

And here is Reductio Ad Absurdum seperately:

Assuming A, B and not B.
I will assume not A.
I will deduce B from B and not B, using Conjuntion Elimination.
I will deduce Not A or B from B, using Disjunction Construction.
I will deduce not B from B and not B, using Conjunction Elimination.
I will deduce Not A from Not A or B and not B, using Disjunction Elimination.
I will deduce A or not A, using Law of excluded Middle.
I will deduce Not A, assuming A or Not A, using Case Analysis.
I will deduce A or Not A implies Not A, using Deduction Theorem.
I will deduce Not A from A or Not A implies Not A and A or Not A.
Last edited by PkmnQ on April 15th, 2019, 12:54 pm, edited 1 time in total.

Code: Select all

``````x = 12, y = 12, rule = AnimatedPixelArt
4.P.qREqWE\$4.2tL3vSvX\$4.qREqREqREP\$4.vS4vXvS2tQ\$2.qWE2.qREqWEK\$2.2vX
2.vXvSvXvStQtL\$qWE2.qWE2.P.K\$2vX2.2vX2.tQ2tLtQ\$qWE4.qWE\$2vX4.2vX\$2.qW
EqWE\$2.4vX!
``````
i like loaf

testitemqlstudop
Posts: 1184
Joined: July 21st, 2016, 11:45 am
Location: in catagolue
Contact:

### Re: Phoenices

In fact, that's called a contrapositive, and it will always imply the original statement.

Hunting
Posts: 1117
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Phoenices

This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:

Code: Select all

``````#C Favorite Gun. Found by me.
x = 4, y = 6, rule = B2e3i4at/S1c23cijn4a
o2bo\$4o3\$4o\$o2bo!``````