### Mirrors

**January 18th, 2017, 3:37 pm**

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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
```

- 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!
```

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!
```

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