### SelfRep rule (WMPVN 4568/456/?)

Posted:

**January 27th, 2011, 6:07 pm**I found this family of rules. Some of its members seem to exhibit self-replicating behavior.

4568/456/4: The basic c/2 ship in this family of rules evolves into a pattern that repeats its structure over time, sort of a spacefiller.

4568/456/5: From here (c > 4) the ship behaves as a ship.

A simple 3x3 square self-replicates endlessly. Contained inside a square. The basic ship is faster than

4568/456/6: Nothing to see here, except for this bigger ship that will play an important role later:

4568/456/7: The bigger ship doesn't work here.

This ship, similar to the basic ship, replicates itself, showing sawtooth-like growth and leaving a trail of basic ships behind on a Sierpinski triangle.

4568/456/8: The bigger ship works again, and will work for any c > 8. When c = 8, it is a basic ship backrake. A collision between two basic ships creates a new, really resilient 2c/17 basic ship frontal rake. This simple pattern shows it all:

I haven't found any interesting behavior for c > 8.

4568/456/4: The basic c/2 ship in this family of rules evolves into a pattern that repeats its structure over time, sort of a spacefiller.

Code: Select all

```
x = 4, y = 3, rule = WMPVN-4568_456_4
3A$2ACB$3A!
```

Code: Select all

```
x = 4, y = 3, rule = WMPVN-4568_456_5
3A$2ACB$3A!
```

Code: Select all

```
x = 3, y = 3, rule = WMPVN-4568_456_5
3A$A.A$3A!
```

Code: Select all

```
x = 9, y = 8, rule = WMPVN-4568_456_6
3.3A$.2ABAB2A$.2ADAD2A$D2A.C.2AD$E.E.E.E.E$E7.E$DE5.ED$CDE3.EDC!
```

This ship, similar to the basic ship, replicates itself, showing sawtooth-like growth and leaving a trail of basic ships behind on a Sierpinski triangle.

Code: Select all

```
x = 5, y = 3, rule = WMPVN-4568_456_7
.C2A$DE3A$FC2A!
```

Code: Select all

```
x = 23, y = 28, rule = WMPVN-4568_456_8
6.3F$3.A.2FEDE$2.3AE2FE$.4A2FED$.ACE2F$3ABD2F$.ACE2F$.4A2FED$2.3AE2FE
$3.A.2FEDE$6.3F8$13.E7.E$12.FDED3.DEDF$12.FEFE3.EFEF$12.4F.F.4F$13.FE
5FEF$14.2AFDF2A$13.3AEBE3A$14.2ACAC2A$15.5A$17.A!
```