PositronicBrain

[Yoel]

A cyclical rule with 2 colors (defined as red and blue) that resembles Seeds and Brian's Brain. It has many guns, stable reflectors and splitters, puffers, rakes, still lifes and oscillators. Like Brian's Brain, it explodes, but not completely chaotically. Local patterns are easily seen and extractable. The rules are as follows (D2b-0a12a13a in my cyclical rules notation):

1. A cell of a certain color is born, when surrounded by 2 cells of the opposite color.
2. A cell survives, if it stands alone, surrounded by 1 cell of the same color and 2 cells of the opposite color, or surrounded by 1 cell of the same color and 3 cells of the opposite color.

Some guns (P6,12,14,16):

Code: Select all

x = 112, y = 83, rule = PositronicBrain
8.AB6.BA72.AB$8.BA6.AB72.BA$13.B.B$12.B3.B$12.B3.B$13.B.B$8.BA6.AB72.
BA$8.AB6.BA72.AB11$11.BA2.AB$5.BA4.AB2.BA$5.AB83.BA$90.AB$10.B$10.B$
90.AB$5.AB83.BA$5.BA4.AB2.BA$11.BA2.AB11$10.BA.AB$BA8.AB.BA$AB7.B5.B
74.BA$8.AB.BAB.BA73.AB3$8.AB.BAB.BA73.AB$AB7.B5.B74.BA$BA8.AB.BA$10.B
A.AB12$13.AB$13.BA$7.AB81.BA$7.BA5.A75.AB$16.A$16.A$7.BA5.A75.AB$7.AB
81.BA$13.BA$13.AB!

A reflector/splitter gun (all periods >=17):

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x = 201, y = 131, rule = PositronicBrain
7$32.B6$27.BA37.A.BA$27.AB32.AB5.AB$61.BA$27.B4.2B9.BA$46.A12.B15.B
15.BA$30.B3.B11.A13.A16.B16.A$34.A9.A15.A16.B16.A64.A$28.AB.B43.B15.B
A$28.BA16.AB2.AB$33.B12.BA2.BA$62.A3.A$60.AB4.B$60.BA$64.2B$35.AB$35.
BA23.AB$60.BA$31.2B$35.AB$30.B4.BA$30.A3.A$49.AB2.AB8.B$49.BA2.BA12.A
B$65.B.BA$36.A15.A9.A$21.A14.A13.A2.B8.B3.B$37.B12.A2.2A$52.AB9.2B4.B
$34.AB$27.BA5.BA32.BA$27.AB.A37.AB4$64.B3$30.B29$26.B6$21.BA41.A.BA$
21.AB36.AB5.AB$59.BA$21.B11.BA16.BA8.2B.2B$36.A8.A8.A12.B17.B17.B$36.
A6.A.A.A6.A6.B7.B17.B17.B$34.A9.3A4.BA16.B17.B17.B61.A$22.AB20.A3.A
13.2B3.B17.B17.B$22.BA2.2A14.AB2.AB$24.B17.BA2.BA$27.A$58.AB$58.BA$
27.AB$29.AB$29.BA27.AB$58.BA$60.BA$29.AB$29.BA$61.A$45.AB2.AB13.B$45.
BA2.BA10.2A2.AB$21.B3.2B38.BA$19.B16.AB16.A$15.A3.B7.B6.A17.A$21.B12.
A17.A$23.2B.2B8.AB16.AB11.B$28.AB$21.BA5.BA36.BA$21.AB.A41.AB4$62.B3$
24.B!

Oscillators (P2,3,4,8,26):

Code: Select all

x = 62, y = 44, rule = PositronicBrain
2$17.B$16.B5$10.AB12.AB2.AB2.AB$7.A2.AB2.B9.BA2.AB2.BA6$21.B.B8.B$4.B
9.B5.B3.B6.ABA6.B$3.ABA5.B3.B14.B2.B16.BABA$4.B7.B17.ABA6.B.B6.A.BABA
2.A$31.B9$29.A$13.ABABAB11.A$11.B.ABABAB.A8.2A$30.B7$7.BA5.AB2.AB2.BA
$7.AB5.AB2.AB2.AB!

[bprentice]

Another excellent rule! Thank you for the clear rule definition.

Brian Prentice

[Yoel]

A new variety of this rule called Jails, in which random patterns turn into networks of periodic or seemingly aperiodic self-confined unbreakable walls. Many patterns, including common guns, reflectors and splitters are compatible with PositronicBrain. The rule string in my cyclical notation is D2b-0a12a13a5n. The only difference from PositronicBrain is that a cell survives if surrounded by 5 cells of any color.

A block seems to explode aperiodically:

Code: Select all

x = 4, y = 6, rule = Jails
2$.2B$.2B!

Eventually periodic breeder:

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x = 19, y = 19, rule = Jails
$15.B5$9.2A$9.2A$7.2B$7.2B5$2.A!

Oscillators (p2,3,4,6,7,8,9,12). Some work in PositronicBrain:

Code: Select all

x = 58, y = 115, rule = Jails
3$38.BA2.BA2.BA$38.AB2.AB2.AB$28.A2.B9.B3.B$18.A7.AB.BA.AB8.B$19.A6.B
A.BA.BA8.B$41.B3.B$38.AB2.AB2.AB$38.BA2.BA2.BA5$32.A$30.A.A.A$31.3A$
29.3A.3A$31.3A$30.A.A.A$32.A5$36.A$34.A.A.A7.B$10.A7.B10.A5.3A$11.A
14.3A15.B2.B$8.A9.B6.A$9.A35.B6$26.A.BABABABA.B$28.BABABABA2$28.A.A4.
B$30.A2$28.BABABABA$26.A.BABABABA.B9$29.BABA$29.BABA2$26.2B6.2A$26.2A
6.2B$26.2B6.2A$26.2A6.2B2$29.ABAB$29.ABAB8$31.B2.B$32.B9$28.2BABAB.B$
29.A.BABAB$28.2B5.A$28.2A4.2B$28.2B4.2A$28.A5.2B$28.BABAB.A$28.B.BABA
2B12$10.B18.BA2.AB$8.BA.ABA15.AB2.BA$8.AB.ABA17.A$7.B6.B$8.AB.ABA20.B
3.A$8.BA.AB12.B8.B$10.B3.BAB$13.ABAB.A12.A$29.AB2.BA$29.BA2.AB!

A universal stretchable loop gun (and oscillator) for all periods p>=14. Works in PositronicBrain as well:

Code: Select all

x = 56, y = 57, rule = Jails
4$8.BA$8.AB$41.BA$11.B29.AB$12.B4.BA$17.AB2.AB11.BA$21.BA11.AB$8.BA3.
AB14.B13.B$16.B13.B10.B2.B$4.AB10.B13.B9.AB2.B$4.BA2.BA3.AB14.B11.B.B
$21.BA$21.AB$10.2B5.BA$9.B2.B4.AB$37.AB7.AB$7.AB3.2B23.BA7.BA$7.BA2.B
A27.B2$39.AB4.BA$39.BA.2B.AB7$7.BA.2B.AB$7.AB4.BA2$13.B27.AB2.AB$6.AB
7.AB23.2B3.BA$6.BA7.BA$35.BA4.B2.B$35.AB5.2B$31.BA$31.AB$10.B.B11.B
14.BA3.AB2.AB$9.B2.BA9.B13.B10.BA$9.B2.B10.B13.B$2.AB6.B13.B14.BA3.AB
$2.BA14.BA11.AB$18.AB11.BA2.BA$35.AB4.B$11.BA29.B$11.AB$44.BA$44.AB!

Photon period quadrupler with photon type shifters (Jails and PositronicBrain):

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x = 79, y = 22, rule = Jails
3$43.BA26.AB$25.BA.BA9.AB2.AB26.BA$6.AB6.BA9.AB.AB4.BA3.BA34.AB$6.BA
4.A.AB4.AB12.AB2.A36.BA$10.A.A8.A14.A.A22.A$9.A2.A2.A5.A17.A23.A$9.A
2.A2.A5.A15.A.A23.A$10.A.A8.A39.A$6.BA4.A.AB4.AB53.BA$6.AB6.BA9.AB.AB
7.BA32.AB2.AB$25.BA.BA7.AB4.AB26.BA$43.BA!

Growing puffer-rake (Jails only):

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x = 77, y = 45, rule = Jails
6$36.A$38.A$38.A$36.A2$27.B$26.3A.A2.A$27.B$39.2A2$38.A2.A6$47.2A2$
46.A2.A2$13.AB$16.B$16.B38.A7.AB$13.AB17.B7.B7.B6.2B5.2B2.B$56.A5.AB
2.B$15.B7.B6.A22.B8.B2.B$32.A29.B.B$32.A30.B$12.A7.A7.A17.A7.A2$10.BA
25.A3.A$13.A26.B2.A$13.A29.A$10.BA29.A!

4-gens delay line and a phase-shifting reflector/splitter (works slightly differently in PositronicBrain, reflecting a different type of photons):

Code: Select all

x = 108, y = 25, rule = Jails
5$44.BA$26.BA.BA9.AB2.AB24.BA$7.AB6.BA9.AB.AB4.BA3.BA28.AB$7.BA6.AB
18.AB$13.A3.A.A$12.A3.A3.A$12.A3.A3.A69.AB4.BA$13.A3.A.A55.AB13.BA4.A
B$7.BA6.AB23.B34.BA$7.AB6.BA9.AB.AB7.BA$26.BA.BA7.AB4.AB$44.BA!

[bprentice]

Yoel,

MCell and Square Cell are designed to support rule families. For each rule family a dialog is used to display and obtain rule parameters and options for a specific member of the family. Can you design such a dialog for your cyclical rule family.

A period 16 ship:

Code: Select all

#Rows = 50
#Columns = 267
x = 267, y = 50, rule = Jails
72.A$74.A106.A$74.A108.A$72.A69.A40.A$4.A139.A36.A$6.A137.A$6.A61.B
2.B70.A$4.A63.A2.A3$B2.B$A2.A180.2B$77.2B7.B.B$89.B55.2B36.B2.B10.B
$76.B2.B5.B.B2.B92.A2.A5.A5.B$76.A2.A10.B53.B2.B10.B34.AB4.B$9.2B7.
B.B55.B2.B8.B55.A2.A5.A5.B35.A3.B$21.B132.AB4.B32.B3.B$8.B2.B5.B.B2.
B54.2B77.A3.B22.A2.A$8.A2.A10.B5.BA124.B3.B24.B2.B$8.B2.B8.B10.A112.
A2.A$31.A112.B2.B36.2B$9.2B17.BA$68.A2.A73.2B85.B$36.A15.A15.B2.B152.
A2.A6.B29.B$228.B3.B.B31.B$59.B7.A2.B11.B47.B26.A7.AB3.BA3.A2.A23.B
25.B.B31.B3.B$60.A3.B15.B.B.B12.A.A28.B.B.B7.B4.A.A15.A9.A2B.2B22.A
11.A14.B.B26.A2.B3.B$15.A4.A10.A4.A10.A4.A8.B3.3B13.3B12.A3.A12.3B13.
3B4.A7.A3.A11.B2.A9.A.ABA7.A7.A6.B6.A5.A11.A9.A3.A3.A3.A3.A3.A7.B$33.
B15.B14.2B.B11.3B.3B27.B.B11.3B.3B2.B2.2B24.AB3.BA5.2B5.3B5.3B4.3A13.
AB40.A2.B.B$65.3B13.3B12.A3.A12.3B13.3B9.A2.A3.A8.A19.A7.A7.A6.B$31.
A48.B.B.B12.A.A28.B.B.B4.2B6.A.A$33.A48.B47.B$33.A$31.A$A$2.A$2.A$A
5$107.B15.B2$105.A$107.A18.B$107.A20.B$105.A22.B$125.AB!

Brian Prentice