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Mirrors

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Mirrors

Postby Rhombic » January 18th, 2017, 3:37 pm

A rule based on biggiemac's idea in the CA Puzzles thread.
@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:
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:
x = 6, y = 6, rule = Mirrors
2.A$A.A$.2A2$4.2B$4.2B!

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:
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:
x = 11, y = 10, rule = Mirrors
4.C$9.2C$9.2C2$6.C3$.A$.2A$A.A!
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Re: Mirrors

Postby Kiran » January 18th, 2017, 7:01 pm

This rule has nice methuselahs:
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.)
x = 5, y = 3, rule = Mirrors
C2.C2$C.C.C!

I wonder who can find the longest lasting one that terminates.
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Re: Mirrors

Postby toroidalet » January 21st, 2017, 11:22 pm

Lots of oscillators, just like extendedlife
p38:
x = 13, y = 1, rule = Mirrors
C4.2AC4.C!

A p179 gun:
x = 5, y = 16, rule = Mirrors
2.C10$.3B$A3.A$.C.C3$2.A!

P58:
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:
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:
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:
x = 18, y = 4, rule = Mirrors
16.AC$9.4C3.A$.A3.4C$CA!

P122:
x = 8, y = 2, rule = Mirrors
4.4C$4C!

P33:
x = 18, y = 8, rule = Mirrors
17.C3$9.4C$5.4C3$C!

P16:
x = 9, y = 6, rule = Mirrors
4.3C$7.2A$2C2.C.C2A3$C!

P12:
x = 5, y = 3, rule = Mirrors
3C$3.2A$C.C2A!
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Re: Mirrors

Postby BlinkerSpawn » January 22nd, 2017, 9:22 am

p97+:
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!
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Re: Mirrors

Postby AbhpzTa » January 22nd, 2017, 1:03 pm

p53+n:
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).
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Re: Mirrors

Postby Rhombic » February 24th, 2017, 1:02 pm

AbhpzTa wrote:p53+n:
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:
x = 16, y = 18, rule = Mirrors
11.2C$15.C6$7.A$7.2A$6.A.A7$C$3.2C!
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Re: Mirrors

Postby Rhombic » March 12th, 2017, 11:02 am

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:
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
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.
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Re: Mirrors

Postby BlinkerSpawn » March 12th, 2017, 1:54 pm

Here's a conduit; repeat time at least 102 depending on how the pi is used:
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:
x = 66, y = 16, rule = Mirrors
3.2C38.2C5$2A15.C22.2A$.2A38.2A$.A39.A23.C5$47.2C3$49.C!
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Re: Mirrors

Postby Rhombic » March 12th, 2017, 3:46 pm

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

Postby BlinkerSpawn » March 12th, 2017, 6:08 pm

Rhombic wrote:Very trivial r-based binary counter:
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:
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!
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Re: Mirrors

Postby Rhombic » March 25th, 2017, 12:41 pm

3-state counter!!
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
x = 12, y = 10, rule = Mirrors
9.2C$10.C$8.C5$10.A$C8.2A$9.A.A!


H-->2G
x = 9, y = 13, rule = Mirrors
7.C6$C3$7.C$.3A4.C$2.A$2.3A!


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

x = 7, y = 8, rule = Mirrors
.C3.C$C5.C4$2.3A$2.A$3.A!
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Re: Mirrors

Postby Rhombic » March 31st, 2017, 2:13 pm

G-->2G:
x = 5, y = 7, rule = Mirrors
3.A$4.A$2.3A3$2B.2C$2B.2C!


Period 148 pi hassler
x = 12, y = 18, rule = Mirrors
C5$2.3A$2.A.A$2.A.A10$11.C!


counting per period:
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:
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!
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Re: Mirrors

Postby Moosey » February 26th, 2019, 4:57 pm

Bump
19p20
x = 7, y = 7, rule = Mirrors
2AC.C2A$3.A$3.A$2.3C$3.A$3.A$2AC.C2A!

10p18
x = 9, y = 3, rule = Mirrors
C.2C.2C.C$.A5.A$.A5.A!

repeat time 58 microreflector:
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:
#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:
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:
x = 13, y = 6, rule = Mirrors
10.2A$3.2C5.ACB$2A$2A$3.2C5.ACB$10.2A!
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My CA rules can be found here

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