Mirrors

For discussion of other cellular automata.
Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Mirrors

A rule based on biggiemac's idea in the CA Puzzles thread.

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``````@RULE Mirrors

@TABLE

n_states:4
neighborhood:Moore
symmetries:permute

var a={0,1,2,3}
var a2=a
var a3=a
var a4=a
var a5=a
var a6=a
var a7=a
var a8=a
var l={1,3}
var l2=l
var l3=l
var l4=l
var l5=l
var l6=l
var l7=l
var l8=l
var d={0,2}
var d2=d
var d3=d
var d4=d
var d5=d
var d6=d
var d7=d
var d8=d

#BIRTH
0,l,l2,l3,d,d2,d3,d4,d5,1
2,a,a2,d,d2,d3,d4,d5,d6,3
2,l,l2,l3,l4,a,a2,a3,a4,3

#SURVIVE
1,l,l2,a,d,d2,d3,d4,d5,1
3,a,d,d2,d3,d4,d5,d6,d7,3
3,l,l2,l3,l4,a,a2,a3,a4,3

#CAT
1,a,a2,a3,a4,a5,a6,a7,a8,0
3,a,a2,a3,a4,a5,a6,a7,a8,2

@COLORS

1 255 255 255
2 35 35 35
3 225 255 255``````
The behaviour of the states 2 and 3, complementary cells, is similar to that of special states in extendedlife, but not quite. Quite a few stable groupings of cells, as well as haplominos, are interesting catalysts or eaters.

- All still lifes in CGoL, when made with the states 2 and 3, are period 2 oscillators. They can therefore change in phase/parity (with the biblock potentially having an in phase or an out of phase combination).
I like to call them g for those with the live state in even generations and u for those with the live state in odd generations, from the group theory (applied to chemistry) nomenclature genau/ungenau.

There immediately is a marvellous application to this!! Pseudo still lifes, like the biblock, can be (g,u), i.e. each island in a different phase. However, for true still lifes to be period 2 oscillators, all the still life has to be in phase with itself - otherwise the cells that make it a true still life will be born, see here:

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``````x = 31, y = 19, rule = Mirrors
2C24.2B\$2C24.2B2\$2C24.2C\$2C24.2C11\$4.2C23.2C\$4.C24.C\$.2C.C21.2B.C\$.2C
.2C20.2B.2C!
``````

^ Proof that block on table is a true still life

Reactions can switch the parity of a SLP2:

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``````x = 6, y = 6, rule = Mirrors
2.A\$A.A\$.2A2\$4.2B\$4.2B!
``````

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``````x = 3, y = 3, rule = Mirrors
.2C\$A2C\$A!
``````
^Glider or two cells change g-block to u-block

Proof of selective response:
A parity changing G to Century:

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``````x = 11, y = 10, rule = Mirrors
4.C\$9.2B\$9.2B2\$6.C3\$.A\$.2A\$A.A!
``````
will function as an eater with same parity if the glider enters at a wrong phase:

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``````x = 11, y = 10, rule = Mirrors
4.C\$9.2C\$9.2C2\$6.C3\$.A\$.2A\$A.A!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Kiran
Posts: 284
Joined: March 4th, 2015, 6:48 pm

Re: Mirrors

This rule has nice methuselahs:

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``````x = 5, y = 3, rule = Mirrors
C.C2\$C.C.C!
``````
This one, at 3292192 generations, is probably not exceptional (larger patterns of defect cells go practically forever.)

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``````x = 5, y = 3, rule = Mirrors
C2.C2\$C.C.C!
``````
I wonder who can find the longest lasting one that terminates.
Kiran Linsuain

toroidalet
Posts: 1037
Joined: August 7th, 2016, 1:48 pm
Location: my computer
Contact:

Re: Mirrors

Lots of oscillators, just like extendedlife
p38:

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``````x = 13, y = 1, rule = Mirrors
C4.2AC4.C!
``````
A p179 gun:

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``````x = 5, y = 16, rule = Mirrors
2.C10\$.3B\$A3.A\$.C.C3\$2.A!
``````
P58:

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``````x = 16, y = 11, rule = Mirrors
14.2A\$14.A\$12.A.A\$12.2A2\$C7.C2A2\$12.2A\$12.A.A\$14.A\$14.2A!
``````
P52:

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``````x = 17, y = 11, rule = Mirrors
15.2A\$15.A\$13.A.A\$8.3A2.2A2\$C8.C.A2\$8.3A2.2A\$13.A.A\$15.A\$15.2A!
``````
P29:

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``````x = 15, y = 11, rule = Mirrors
13.2A\$13.A\$11.A.A\$11.2A2\$C6.C2A2\$11.2A\$11.A.A\$13.A\$13.2A!
``````
P1134:

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``````x = 18, y = 4, rule = Mirrors
16.AC\$9.4C3.A\$.A3.4C\$CA!
``````
P122:

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``````x = 8, y = 2, rule = Mirrors
4.4C\$4C!
``````
P33:

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``````x = 18, y = 8, rule = Mirrors
17.C3\$9.4C\$5.4C3\$C!
``````
P16:

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``````x = 9, y = 6, rule = Mirrors
4.3C\$7.2A\$2C2.C.C2A3\$C!
``````
P12:

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``````x = 5, y = 3, rule = Mirrors
3C\$3.2A\$C.C2A!
``````
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

Posts: 1930
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Mirrors

p97+:

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``````x = 178, y = 178, rule = Mirrors
88.3A\$88.A\$81.A7.A\$81.C\$77.C4A\$77.A3.C\$76.2A.2A24.C\$76.A.A\$102.C\$76.A
10.2A\$75.2A9.2A\$75.2A11.A5\$82.A\$82.A.A\$82.2A15\$111.2A\$111.A.A\$111.A5\$
59.A\$57.2A\$58.2A15\$136.A\$135.2A\$135.A.A5\$34.A\$33.A\$33.3A6\$6.C3\$8.C
157.2A\$166.3A.2A\$171.2AC\$170.A2.A\$171.A.A\$171.A.A\$172.CACA\$159.3A\$
159.A\$160.A2\$167.A\$A166.2A\$A.A163.A.A7.2A\$2A7.A.A163.A.A\$9.2A166.A\$
10.A2\$17.A\$18.A\$16.3A\$2.ACAC\$4.A.A\$4.A.A\$4.A2.A\$4.C2A\$6.2A.3A\$10.2A
157.C3\$171.C6\$142.3A\$144.A\$143.A5\$40.A.A\$41.2A\$41.A15\$118.2A\$119.2A\$
118.A5\$66.A\$64.A.A\$65.2A15\$94.2A\$93.A.A\$95.A5\$89.A11.2A\$90.2A9.2A\$89.
2A10.A\$75.C\$99.A.A\$72.C24.2A.2A\$96.C3.A\$96.4AC\$96.C\$88.A7.A\$89.A\$87.
3A!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

AbhpzTa
Posts: 478
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Mirrors

p53+n:

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``````x = 62, y = 69, rule = Mirrors
5.2C6\$C\$C\$4.C\$10.2A\$10.A.A\$10.A3\$.2A\$.BA2\$10.A\$11.2A\$10.2A3\$24.A\$23.
2A\$23.A.A6\$24.A\$25.A\$23.3A4\$36.3A\$36.A\$37.A6\$36.A.A\$37.2A\$37.A3\$50.2A
\$49.2A\$51.A2\$59.AB\$59.2A3\$51.A\$49.A.A\$50.2A\$57.C\$61.C\$61.C6\$55.2C!``````
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).

Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Re: Mirrors

AbhpzTa wrote:p53+n:

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``````x = 62, y = 69, rule = Mirrors
5.2C6\$C\$C\$4.C\$10.2A\$10.A.A\$10.A3\$.2A\$.BA2\$10.A\$11.2A\$10.2A3\$24.A\$23.
2A\$23.A.A6\$24.A\$25.A\$23.3A4\$36.3A\$36.A\$37.A6\$36.A.A\$37.2A\$37.A3\$50.2A
\$49.2A\$51.A2\$59.AB\$59.2A3\$51.A\$49.A.A\$50.2A\$57.C\$61.C\$61.C6\$55.2C!``````
Reflector based-oscillator:

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``````x = 16, y = 18, rule = Mirrors
11.2C\$15.C6\$7.A\$7.2A\$6.A.A7\$C\$3.2C!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Re: Mirrors

Code: Select all

``````x = 114, y = 24, rule = Mirrors
\$7.2A58.2A\$7.2A10.C31.C15.2A10.C29.C\$2A30.2A\$2A21.C8.2A21.C27.C29.C\$
16.C31.C27.C29.C4\$20.A31.A27.A29.A\$19.3A29.3A25.3A27.3A\$19.A31.A27.A
29.A12\$18.2C30.2C26.2C28.2C!
``````
Studying conduits 1, 2, 3 and 4:

Conduit 1: block A + block B + r ==> glider + conduit 4
Conduit 2: block A + r ==> conduit 2
Conduit 3: block B + r ==> conduit 4
Conduit 4: r ==> conduit 4

quite sparky anyway, so probably more complicated conduits are yet to be found:

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``````x = 59, y = 35, rule = Mirrors
4\$36.2A10.C\$12.C23.2A\$23.2A27.C\$16.C6.2A20.C\$9.C3\$49.A\$13.A34.3A\$12.
3A33.A\$12.A11\$47.2C\$11.2C!
``````
---------
R-eater

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``````x = 26, y = 13, rule = Mirrors
16.C3.C\$C.C2\$C.C22.C\$18.C2.C6\$24.A\$23.3A\$25.A!
``````
---------
Last edited by Rhombic on March 14th, 2017, 12:32 pm, edited 1 time in total.
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Posts: 1930
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Mirrors

Here's a conduit; repeat time at least 102 depending on how the pi is used:

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``````x = 17, y = 33, rule = Mirrors
2.2A\$2.2A7\$C14\$16.C\$16.C7\$11.A\$10.3A\$10.A!
``````
R-to-B and R-to-H:

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``````x = 66, y = 16, rule = Mirrors
3.2C38.2C5\$2A15.C22.2A\$.2A38.2A\$.A39.A23.C5\$47.2C3\$49.C!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Re: Mirrors

BlinkerSpawn wrote:Here's a conduit; repeat time at least 102 depending on how the pi is used:

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``````x = 17, y = 33, rule = Mirrors
2.2A\$2.2A7\$C14\$16.C\$16.C7\$11.A\$10.3A\$10.A!
``````
R-to-B and R-to-H:

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``````x = 66, y = 16, rule = Mirrors
3.2C38.2C5\$2A15.C22.2A\$.2A38.2A\$.A39.A23.C5\$47.2C3\$49.C!
``````
Very trivial r-based binary counter:

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``````x = 54, y = 37, rule = Mirrors
8.C33.B2A\$10.C31.2AB3\$2.2A32.2A\$2.2A32.2A\$13.2C32.2C4\$18.2C32.2C2\$C
17.2C14.C17.2C14\$16.C33.C\$16.C33.C7\$11.A33.A\$10.3A31.3A\$10.A33.A!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Posts: 1930
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Mirrors

Rhombic wrote:Very trivial r-based binary counter:

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``````x = 54, y = 37, rule = Mirrors
8.C33.B2A\$10.C31.2AB3\$2.2A32.2A\$2.2A32.2A\$13.2C32.2C4\$18.2C32.2C2\$C
17.2C14.C17.2C14\$16.C33.C\$16.C33.C7\$11.A33.A\$10.3A31.3A\$10.A33.A!
``````
Better:

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``````x = 68, y = 24, rule = Mirrors
17.C31.A17.C\$48.A.A\$48.A.A\$49.A3\$C49.C7\$17.C49.C\$17.C49.C7\$12.A49.A\$
11.3A47.3A\$11.A49.A!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Re: Mirrors

3-state counter!!

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``````x = 122, y = 15, rule = Mirrors
89.A\$40.A48.A\$39.A.A47.A\$16.C21.A2.A24.C49.C\$39.2A44.3A3.3A\$.C5.C43.C
5.C43.C5.C\$4.C11.2B36.C11.2B21.A14.C11.2B\$16.B49.B22.A26.B\$17.C49.C
21.A27.C3\$C49.C49.C\$19.3A47.3A47.3A\$19.A49.A49.A\$8.2C10.A37.2C10.A37.
2C10.A!
``````
parity-switching G-->2G

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``````x = 12, y = 10, rule = Mirrors
9.2C\$10.C\$8.C5\$10.A\$C8.2A\$9.A.A!
``````
H-->2G

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``````x = 9, y = 13, rule = Mirrors
7.C6\$C3\$7.C\$.3A4.C\$2.A\$2.3A!
``````
Reflectors:

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``````x = 13, y = 16, rule = Mirrors
4.C\$5.C2\$12.C5\$.C3\$6.2A\$5.2A\$7.A2\$C!
``````

Code: Select all

``````x = 7, y = 8, rule = Mirrors
.C3.C\$C5.C4\$2.3A\$2.A\$3.A!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic
Posts: 1057
Joined: June 1st, 2013, 5:41 pm

Re: Mirrors

G-->2G:

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``````x = 5, y = 7, rule = Mirrors
3.A\$4.A\$2.3A3\$2B.2C\$2B.2C!
``````
Period 148 pi hassler

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``````x = 12, y = 18, rule = Mirrors
C5\$2.3A\$2.A.A\$2.A.A10\$11.C!
``````
counting per period:

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``````x = 24, y = 18, rule = Mirrors
C5\$2.3A\$2.A.A\$2.A.A2\$19.C\$17.C\$21.C\$20.C\$23.C\$22.C3\$11.C!
``````
Yet another glider binary counter:

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``````x = 35, y = 31, rule = Mirrors
5.A\$5.A\$5.A2\$30.C3.C\$29.C2\$2C6.C16.C\$11.2C12.C4.A\$2C6.C21.2A\$29.A.A4\$
5.A\$5.A\$5.A8\$30.C3.C\$29.C2\$2C6.C16.C\$11.2C12.C4.A\$2C6.C21.2A\$29.A.A!
``````
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Moosey
Posts: 2798
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

Re: Mirrors

Bump
19p20

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``````x = 7, y = 7, rule = Mirrors
2AC.C2A\$3.A\$3.A\$2.3C\$3.A\$3.A\$2AC.C2A!
``````
10p18

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``````x = 9, y = 3, rule = Mirrors
C.2C.2C.C\$.A5.A\$.A5.A!
``````
repeat time 58 microreflector:

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``````x = 22, y = 31, rule = Mirrors
2.A\$A.A\$.2A12\$16.A\$17.A\$15.3A6\$17.CA\$18.BC5\$21.C\$20.AB\$20.C!
``````
instructions for UCC, proof of concept:

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``````#C based on a p2 splitter by rhombic
x = 120, y = 178, rule = Mirrors
3.A\$4.A\$2.3A3\$2B.2C\$2B.2C18\$11.2B.2C\$11.2B.2C18\$22.2B.2C\$22.2B.2C18\$
33.2B.2C\$33.2B.2C37\$63.2B.2C\$63.2B.2C18\$74.2B.2C\$74.2B.2C37\$104.2B.2C
\$104.2B.2C18\$115.2B.2C\$115.2B.2C!
``````
They say you win some and you lose some:

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``````x = 14, y = 12, rule = Mirrors
7.A5.C\$8.A4.C\$6.3A3\$C\$.C5.2A\$7.2A4\$9.C!
``````
some lower period oscillators:

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``````x = 13, y = 6, rule = Mirrors
10.2A\$3.2C5.ACB\$2A\$2A\$3.2C5.ACB\$10.2A!
``````
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"