Smallest Known Oscillators to p106 (and Beyond)

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Freywa
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Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 3rd, 2021, 6:26 am

Given David Raucci's recent discoveries of several small oscillators above the snark limit (p43) and the dishevelled state of the oscillator page on the LifeWiki, I made the following stamp collection of the smallest known non-trivial oscillators:

Code: Select all

x = 290, y = 679, rule = LifeSuper
.D19.3D17.3D19.D16.5D16.3D16.5D16.3D17.3D17.D3.3D$2D18.D3.D15.D3.D17.
2D16.D19.D3.D19.D15.D3.D15.D3.D15.2D2.D3.D$.D22.D19.D16.D.D16.D19.D
22.D16.D3.D15.D3.D16.D2.D3.D$.D21.D18.2D16.D2.D17.3D16.4D19.D17.3D17.
4D16.D2.D.D.D$.D20.D21.D15.5D19.D15.D3.D17.D17.D3.D19.D16.D2.D3.D$.D
19.D18.D3.D18.D16.D3.D15.D3.D17.D17.D3.D15.D3.D16.D2.D3.D$3D17.5D16.
3D19.D17.3D17.3D18.D18.3D17.3D16.3D2.3D2$200B2$2A19.A22.A16.2A17.2A
23.2A17.2A16.2B17.2A19.B2A$2A18.BAB20.BAB14.A2.A16.A.B21.B2A2B15.2A
16.3B17.A18.2B.A2B$21.A22.AB14.A.A.AB15.B2A21.4B31.2B2AB17.A.2A15.BA
5B$43.2A16.A.BAB15.4B21.A2B15.4A12.2B2ABA15.2A.A.A13.4BA2BA$.A39.A.2B
17.3BA17.ABA15.B3.ABAB11.2A.A.B2.A12.4B.A15.B.2B.A12.BABA2BAB$A.A37.A
4BA16.ABA19.3B13.2AB.A.BA12.2A.A3BA.A13.A.4B13.3B3A13.2AB.BA$.A38.AB.
2B40.ABA12.2ABA2B17.A.A2.A15.AB2A2B10.2A.2B3.2A12.B.B.B.B$42.3A41.3B
12.3B2A17.A.3A17.B2A2B10.A2.A.2A.A15.AB.B2A$43.B20.B22.ABA11.4B19.A
20.3B14.2A.A2.A14.BA2BABAB$63.2AB22.BAB34.A20.2B18.2A15.A2BA4B$63.BAB
A21.2B.A32.2A57.5BAB$61.AB2.2BA22.2A92.2BA.2B$60.B2A2.BA119.2AB$61.4B
59.2A$62.ABA58.A.A$63.A57.3A.A.2A$120.A4.A.BA$121.3A.A2B$123.A.A$123.
4B$124.B2A$122.4B$122.2A$123.A$120.3A$120.A2$123.2A$123.A.A.2A.A$125.
A.A.2A$124.ABA$124.3B$125.AB$124.BA$124.3B$124.ABA$120.2A.A.A$120.A.
2A.A.A$126.2A2$120.A.A$120.2A.A$123.A2.2A$120.2A.A.A.A$120.AB.A2BA$
122.AB.2B$121.3BAB$121.B3A2B$122.4B$125.B2A$125.BA.A$128.A$128.2A4$.D
3.D15.D3.3D13.D3.3D13.D5.D13.D2.5D12.D3.3D13.D.5D13.D3.3D13.D3.3D13.
3F3.3F$2D2.2D14.2D2.D3.D11.2D2.D3.D11.2D4.2D12.2D2.D15.2D2.D3.D11.2D
5.D12.2D2.D3.D11.2D2.D3.D11.F3.F.F3.F$.D3.D15.D6.D12.D6.D12.D3.D.D13.
D2.D16.D2.D16.D4.D14.D2.D3.D12.D2.D3.D15.F.F3.F$.D3.D15.D5.D13.D4.2D
13.D2.D2.D13.D3.3D13.D2.4D13.D4.D14.D3.3D13.D3.4D14.F2.F.F.F$.D3.D15.
D4.D14.D6.D12.D2.5D12.D6.D12.D2.D3.D12.D3.D15.D2.D3.D12.D6.D13.F3.F3.
F$.D3.D15.D3.D15.D2.D3.D12.D5.D13.D2.D3.D12.D2.D3.D12.D3.D15.D2.D3.D
12.D2.D3.D12.F4.F3.F$3D.3D13.3D.5D11.3D2.3D12.3D4.D12.3D2.3D12.3D2.3D
12.3D2.D14.3D2.3D12.3D2.3D12.5F2.3F2$200B2$3.A17.A24.2A13.2B.2A18.B
17.B17.A11.A8.4B15.D7.D14.2A$.3A17.3A7.2A12.B2AB11.6BA16.3B15.4B15.3A
7.3A8.3BAB15.D5.D14.A2.A$A3.2A18.A6.A14.2B12.2B2ABAB16.3B15.3A3B16.A
5.A10.4ABA16.D3.D13.BA.A.A$.3A2.A16.AB3.BA.A15.6B7.2BABA2B15.2BA2B13.
8B14.A2B4.2A9.3A.A.AB15.D.D14.BAB.A$3.A.A.A.2A.A10.A2BA.B2A15.BABA5BA
26.2BA2B14.3B2AB2A13.BA7B10.B3.ABAB15.D15.A3B$3.3A.A.A.2A12.BA2B12.B
4.BA3BA3BAB3.2BABA2B14.2BABA2B13.2BABAB2AB13.3B2AB17.A2B14.D.D15.ABA$
3.3B2A16.A2BAB11.2AB.2B.A4B2ABA4.2B2ABAB14.3BA3B13.BA7B13.3B2A3B14.2A
2B3.B9.D3.D17.D$2.5BAB15.2BAB12.2A2B3A2.3BA3B4.6BA13.4BA4B12.BA4BAB
14.4B.4B12.B2A2B.A3B7.D5.D16.2A$2.6B14.A2B.4B11.B.4B2.2A4B6.2B.2A14.
4BA4B11.2BA4BA16.3B2A3B13.2A2.ABAB2A5.D7.D13.A4BA$3.5B13.A.2A3.2A13.B
A3BA32.3BA3B13.B2A2BA19.B2A3B17.4B2A26.BA4BAB$4.2B15.A6.A14.5BA32.2BA
BA2B13.B2AB19.7BAB17.5B26.BA4BAB$3.2A15.2A7.3A11.2BA3B33.2BA2B15.B21.
2A4.2BA19.2B29.A2BA$3.A27.A11.3B2AB33.2BA2B38.A5.A15.A2BA30.A.A2.A.A$
4.A39.2BA2B34.3B36.3A7.3A11.BA3B30.2A4.2A$3.2A39.5B34.3B36.A11.A11.A
4BA$44.3AB36.B59.BA.A.B2A$45.B97.2ABA3.B$143.3B$143.4B$143.A2BAB$145.
2A3$148.2A.A$148.A.2A$145.2A.A3.2A$143.A2.A.B3A2.A$143.2A2.BA2.A.A$
147.2B2A2.2A$147.B2.A.A$146.B3.A.A$145.3A3.A$143.AB.2B$143.A4BA$144.A
.2B$146.2A$147.AB$146.BAB$147.A4$.3F3.F13.3D3.3D11.3D3.3D21.3F5.F11.
3D2.5D10.3F3.3F11.3D2.5D20.3F3.3F11.3D3.3D21.3D3.3D$F3.F.2F12.D3.D.D
3.D9.D3.D.D3.D19.F3.F3.2F10.D3.D.D13.F3.F.F3.F9.D3.D5.D19.F3.F.F3.F9.
D3.D.D3.D19.D3.D.D3.D$4.F2.F16.D5.D13.D5.D23.F2.F.F14.D.D17.F.F17.D4.
D24.F.F3.F13.D.D3.D23.D.D3.D$3.F3.F15.D5.D13.D4.2D23.F2.F2.F13.D3.3D
13.F2.4F13.D5.D23.F3.3F13.D3.4D21.2D2.D.D.D$2.F4.F14.D5.D13.D7.D21.F
3.5F11.D7.D11.F3.F3.F11.D5.D23.F3.F3.F11.D7.D23.D.D3.D$.F5.F13.D5.D
13.D4.D3.D20.F7.F11.D4.D3.D10.F4.F3.F10.D6.D22.F4.F3.F10.D4.D3.D19.D
3.D.D3.D$5F.3F11.5D.5D9.5D2.3D20.5F4.F10.5D2.3D10.5F2.3F10.5D3.D21.5F
2.3F10.5D2.3D21.3D3.3D2$230B2$5.A16.A25.2A23.A15.A3.2A5.2A3.A8.2A29.
2A18.2A25.A19.2A$4.BAB15.3A24.A22.BAB13.A.A2.A7.A2.A.A6.A2.A4.2A21.B
2A2B15.A2.A24.3A16.B2A2B$4.BA19.A22.A23.BA14.A.A4.A3.A4.A.A6.A.2A4.A
23.4B13.AB.A.A27.A16.4B$5.2A17.2A22.4A21.2A14.A.5A3.5A.A6.2A2.A.A3.A
20.6B13.3B.A27.2A4.B12.4B$5.2B.A15.5B.2B19.A7.2A12.2B.A14.A11.A10.AB
2.4A.A18.7B13.AB2A28.8B10.4B$4.A4BA16.BA4B14.3AB8.B.A11.A4BA8.2A2.A2.
B2A3.2AB2.A9.A.BA3.A.A17.7B15.A2B30.6B3.BA5.4B$5.2B.BA15.BABA4B9.2A.A
2.AB2.3B.3B.A.2A9.2B.BA8.A2.A.3BA2B.2BA3B.A9.2A2.A.A.2A15.3B2A3B18.DB
3.B20.B.6BA4BA.A3.5B$A4.3A16.BA3BA4B6.A2.A.2A.5B2A4B2A.A2.A7.3A11.A.
2A.5B.5B.2A10.A.2ABAB.AB13.5B2A3B17.7B18.2A6B2A5BA4.5B$3A3.B15.4BA2BA
3B7.2A.A.8BABA5B.A.2A8.B11.2A5.3B3.3B11.5A3.BA2B13.2BA4BA6B11.2B.B2A
4B.2B15.2A7BA3B.B4.7B$3.A2.D2.2A10.5BA2BA3B10.A3.6BAB2A3B2.A10.D13.A
4.5B.5B9.A2.B.AC3A3B13.2BA3BA8B9.2A2B2ABA5B2A15.3B.7B7.7B$2.2A.B.BA.A
11.5B2A3B11.2A2.7B2A3B2.2A9.2B13.A.AB.5B.5B7.A2.AB.BD2.2B2A2B12.2B2A
7B3A2B8.2AB.BABA3B.B2A16.B3.B12.7B$2.7BA14.8B16.6BA4B13.3B13.2AB.5B.
5B7.2A.A.2A.2A2BA2.AB4.4B2.7B2.3BA5B8.B.4BA4B.B11.2A7.7B7.7B$4.B2A.B
14.9B17.3B3.B.B12.2B2AB14.5BA2B.2BA3B9.A.2A.A4.3A5.12B4.9B10.3B.BAB7.
2A4.B2AB4.6BA3B.B4.2A3B2A$4.BA2B4A11.8B18.B.B2.3B13.2B2ABA14.3B3A3B3A
2B9.A2.A2.4A7.2A10B6.5BA3B24.A5.4B3.5B2A5BA3.2B3A2B$4.BABA4.A9.9B17.
5B.B2AB13.4B.A13.7B.6B10.A2BA.A3.A6.2A5B2A2B8.BAB2A3B.B7.3B.BAB8.A.AB
.4B2.2B.5BA4BA.A3.A3BA$5.2B.BA.A10.8B18.5B2.2A16.A.4B14.3B3.3B.B2A6.A
.A2.A.A2.2A7.B.3B2ABAB8.2B2A5B2A3.B.4BA4B.B6.2AB.3B3.3B.6B3.BA4.BABAB
$8.2A.2A9.3B2A5B16.B3AB21.AB2A2B11.5B2.4B.BA.A5.2A4.A14.3BA5B6.10B2A
2.2AB.BABA3B.B2A7.6B.5B.5B10.BA2B$21.3BA2BA5B15.B3AB2.2A18.B2A2B11.2A
4.4B5.A27.9B4.12B3.2A2B2ABA5B2A7.13B3.B11.4B$21.3BA2BA4B16.5B.ABAB17.
3B14.A5.B2AB4.2A27.5BA3B2.7B2.4B4.2B.B2A4B.2B8.6B.6B16.4B$20.4BA3BAB
19.B.B2.3B19.2B11.3A7.2A35.2B3A7B2A2B14.7B11.3BA2B.2BA3B15.4B$21.4BAB
AB20.3B3.B.B31.A47.8BA3BA2B15.B3.B11.3B3AB.B3A3B13.B2A2B$22.4BAB20.8B
3A79.6BA4BA2B32.6B.6B15.2A$22.2B.5B13.2A2.4B3A5B2.2A78.3B2A5B35.4B.4B
$28.2A13.A3.3BA5BA3B2.A79.3B2A3B36.3B3.3B$28.A11.2A.A.5BABA2B2A4B.A.
2A76.7B37.2B5.2B$29.3A8.A2.A.2A.3BA3BA3B2A.A2.A75.7B37.BA2B3.2BAB$31.
A10.2A.A2.AB2.3B.3B.A.2A77.6B38.A.A5.A.A$46.3AB8.B.A80.4B41.A7.A$51.A
7.2A80.2B2AB$48.4A91.2A$48.A$49.A$48.2A4$.3D3.D13.3D3.3D11.3F3.3F11.
3D5.D11.3D2.5D10.3D3.3D11.3D2.5D30.3D3.3D11.3F3.3F13.D3.3D$D3.D.2D12.
D3.D.D3.D9.F3.F.F3.F9.D3.D3.2D10.D3.D.D13.D3.D.D3.D9.D3.D5.D29.D3.D.D
3.D9.F3.F.F3.F11.2D2.D3.D$4.D2.D16.D5.D13.F5.F13.D2.D.D14.D.D17.D.D
17.D4.D34.D.D3.D13.F.F3.F10.D.D2.D3.D$2.2D3.D14.2D5.D12.2F4.2F12.2D2.
D2.D12.2D3.3D12.2D2.4D12.2D5.D32.2D3.3D12.2F3.4F9.D2.D2.D.D.D$4.D2.D
16.D3.D15.F5.F13.D.5D13.D5.D13.D.D3.D13.D3.D35.D.D3.D13.F5.F9.5D.D3.D
$D3.D2.D12.D3.D2.D12.F3.F.F3.F9.D3.D4.D10.D3.D.D3.D9.D3.D.D3.D9.D3.D
3.D31.D3.D.D3.D9.F3.F.F3.F12.D2.D3.D$.3D2.3D12.3D2.5D10.3F3.3F11.3D5.
D11.3D3.3D11.3D3.3D11.3D4.D32.3D3.3D11.3F3.3F13.D3.3D2$220B2$5.2A7.2A
11.2B20.A10.D7.D18.2A11.2A29.2A11.2A14.D7.D16.A18.3B.B$4.B2A2B3.2B2AB
10.3B18.BAB10.D5.D18.B2AB11.A6.B21.B2A2B7.2B2AB14.D5.D16.BAB17.6B$5.
4B3.4B9.2B2AB19.AB11.D3.D13.2A4.3B12.A.AB2.3B21.4B7.4B16.D3.D18.AB14.
2B.8B$4.6B.6B8.2B2ABA17.2A13.D.D14.A.A4.B14.2AB.5B21.4B5.4B18.D.D18.
2A14.2A8B2A$2.8B.8B7.4B.A14.A.2B14.D16.AB2.5B13.5BA3B14.A4.6B3.6B4.A
13.D17.A.2B14.2A7BA2B$.9B.9B8.A.4B11.A4BA3.2A7.D.D16.5BA4B12.3B2A4B
12.A.A2.3BA4B.4BA3B2.A.A11.D.D15.A4BA14.2B.8BA$.4BA4B.4BA4B9.AB2A2B
10.AB.2B3.A.A6.D3.D15.4B2A4B12.4BA4B11.A2.A5BAB2AB.B2ABA5BA2.A9.D3.D
14.AB.2B18.4B2ABAB$.3BABA3B.3BABA3B10.B2A2B12.3A3.A7.D5.D14.5BA4B13.
6B14.2A2.8BA.A8B2.2A9.D5.D15.3A3.2A13.4B2A3B$.3BA2BA2B.2BA2BA3B10.3B
15.B3.2A6.D7.D14.2B2A3B.B2A11.5B16.B2.6BABA.ABA6B2.B9.D7.D15.B3.B2AB
12.10B$.4B2A3B.3B2A4B3.2A6.2B16.D.2B31.6B.BA.A9.5B17.3B.6BAB.BA6B.3B
34.D3.2B13.10B$.3BA4B3.4BA3B4.A5.B18.5B31.4B5.A8.6B12.B3.5B2.6B.6B2.
5B3.B28.6B13.10B$9B3.9B3.A.AB2.4B15.6B31.4B4.2A5.4BA4B10.2AB.6B3.5B.
5B3.6B.B2A24.A5BABAB12.10B$9B3.9B4.2AB.2BA4B12.BA5B26.2A4.4B10.4B2A3B
10.2A9B2.5B.5B2.9B2A23.BA3BA3BAB4.B8.3B2A4B$.3BA4B3.4BA3B7.4BA6B11.2A
3B28.A5.4B10.3BA5B10.4B2A6B.4B.4B.6B2A4B25.AB2A4BA.2B.B2A7.BAB2A4B$.
4B2A3B.3B2A4B7.3BABA6B5.2A.A.A.3A28.A.AB.6B10.5B.B2A9.13B.2B3.2B.13B
25.3BA3B2.3A2B2A7.A8B.2B$.3BA2BA2B.2BA2BA3B7.4BA6B6.A.2A.A.A.A29.2AB.
3B2A2B10.3B2.BA.A10.3BABA6B7.6BABA3B28.4B2A2.4B.B9.2BA7B2A$.3BABA3B.
3BABA3B8.2BABA5B12.A2.3A29.4BA5B10.B6.A11.2BA2BA5B7.5BA2BA2B35.A3BAB
11.2A8B2A$.4BA4B.4BA4B8.7B.B14.2A3.A28.4B2A4B17.2A11.2B2A5B9.5B2A2B
36.A5B11.8B.2B$.9B.9B8.7B18.3A29.4BA5B93.3BA2B13.6B$2.8B.8B10.7B.B15.
A33.5B2.BA29.2B2A5B9.5B2A2B36.B2A3B14.B.3B$4.6B.6B12.8B2A50.B4.A.A27.
2BA2BA5B7.5BA2BA2B35.2BA2B$5.4B3.4B14.5B.B2A49.3B4.2A26.3BABA6B7.6BAB
A3B34.5B$4.B2A2B3.2B2AB14.B2.B2.B49.B2AB30.13B.2B3.2B.13B33.B3A$5.2A
7.2A17.2B34.2A17.2A31.4B2A6B.4B.4B.6B2A4B35.B$33.3B33.A.A48.2A9B2.5B.
5B2.9B2A$31.2B3A35.A4.2A42.2AB.6B3.5B.5B3.6B.B2A$31.2B3AB30.4A.2A2.A
2.A41.B3.5B2.6B.6B2.5B3.B75.2A22.R3.3R$32.B3A.B29.A2.A.B.A.A.2A46.3B.
6BAB.BA6B.3B80.A2.2A18.2R2.R3.R$34.B.3AB29.BABABA.A49.B2.6BABA.ABA6B
2.B81.A.A.A16.R.R2.R3.R$35.B3A2B29.B2ABA.A48.2A2.8BA.A8B2.2A79.2A.A2.
A11.A2.R2.R3.4R$36.3A2B30.2B.BA48.A2.A5BAB2AB.B2ABA5BA2.A77.A2.3B2A9.
3A2.5R5.R$36.3B31.3B52.A.A2.3BA4B.4BA3B2.A.A79.2A3BA9.A8.R2.R3.R$37.
2B22.2A6.4B53.A4.6B3.6B4.A77.3A2.3BAB8.2A7.R3.3R$62.A6.2BA3B57.4B5.4B
83.A2.3A2BA6.5B$62.A.AB3.B2A3B56.4B7.4B85.A.B.B5.A4B$63.2AB.10B53.B2A
2B7.2B2AB85.A.A2B3.BA5B11.2A$65.12BA53.2A11.2A83.3A3.2BA2BA7B6.2A3.A$
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222.4B.4B$31.5B.5B220.5B3.5B$30.6B.6B219.2A9.2A$31.5B.5B221.A9.A$30.
6B.6B217.3A11.3A$30.6B.6B217.A15.A$30.6B.6B$30.6B.6B$30.6B.6B$30.6B.
6B$30.6B.6B$30.B2ABAB.BAB2AB$30.BA2BAB.BA2BAB$31.B3AB.B3AB$30.13B$31.
12B$31.12B$32.4B.5B$30.13B$30.6B.5B$30.4B2.7B$30.2B2AB.7B$32.2A2.7B$
38.3B$38.3B$39.B$40.D.BA$40.BA2BA$36.2A2.2B.AB$36.A.BA.3A$37.A3B.AB$
38.3BA$37.B3AB$38.A.A.A$41.2A4$48.R3.3R3.3R$47.2R2.R3.R.R3.R$48.R2.R
3.R5.R$48.R2.R.R.R4.R$48.R2.R3.R3.R$48.R2.R3.R2.R$.R3.3R3.R35.3R2.3R
2.5R19.R3.3R3.3R17.F3.3F5.F17.F3.3F2.5F$2R2.R3.R.2R68.2R2.R3.R.R3.R
15.2F2.F3.F3.2F16.2F2.F3.F.F$.R2.R3.R2.R69.R2.R3.R5.R16.F2.F3.F2.F.F
17.F2.F3.F.F$.R2.R.R.R2.R25.4B40.R2.R.R.R3.2R17.F2.F.F.F.F2.F17.F2.F.
F.F2.3F$.R2.R3.R2.R25.3B2A14.A24.R2.R3.R5.R16.F2.F3.F.5F16.F2.F3.F5.F
$.R2.R3.R2.R24.2A2B2A12.3A24.R2.R3.R.R3.R16.F2.F3.F4.F17.F2.F3.F.F3.F
$3R2.3R2.3R23.2AB.A.2A9.A26.3R2.3R3.3R16.3F2.3F5.F16.3F2.3F3.3F$37.B
3.3AB8.2A$30B12.3B5.5B25.90B$41.4B3.5B$3.2M35.B2A4B2A5B29.2M30.A30.2A
$4.M36.2A2.3BA6B29.M29.ABAB28.A3.2A$2.M31.2A9.4BA4B28.M31.5B25.A.A3.A
$2.5M28.A11.B2A3B29.5M27.2BA2B21.2A.A.A.2A.A$7.M27.A.AB2.B5.5B35.M25.
A2BA2B21.A.2A.A.A.A$4.3M29.2AB.3B3.7B31.3M26.4BAB25.3BAB$3.M34.6B.4B.
4B18.2A9.M29.4BAB22.3A4B.A72.A$3.4M31.10B3.4B16.BA2BA7.4M26.A3BAB22.A
2.7BA69.A.A$.2M3.M31.2B2A5B5.4B16.4B5.2M3.M24.B.B3A2.6B17.A.4A.2BA70.
A$M2.3M33.A2BA3B7.4B16.3B4.M2.3M24.2A5B2.3A4B17.2A.B3.A$2M.M35.BABA4B
7.4B10.B3.AB2A4.2M.M26.2AB.2B.BA3B2ABA24.2D68.5A$3.M36.BA6B7.4B8.2AB.
A.AB8.M27.B4.2BA7BA23.2B46.2A20.A4.A$3.2M35.3B2.4B7.4B7.A4BA10.2M31.
2BA6BA22.6B45.A10.3B9.BAB.A$40.3B3.4B7.4B7.3BAB44.2BA2BA23.10B43.A.AB
4.8B7.B2A.A2.A$37.A2BA6.4B7.4B6.A2BA44.2B5.D20.4BA4BA4B42.2AB.B.9B5.A
4B.A.A.A$36.BA3B7.4B7.4B3.3B46.B2AB4.2B18.3B2AB4AB2A3B43.8BA4B4.ABAB
3.A2.A$36.A4BA7.4B7.4B2.3B47.2A5.3B18.4BA4BA4B43.8BABA3B4.A2BA2.2A$
34.BA.A.B2A8.4B7.6BAB52.2B2AB20.10B45.7BA2BA8B2A$33.2ABA3.B10.4B7.4BA
BAB51.2B2ABA21.6B35.2A9.9BA2BA7B$33.3B16.4B7.3BA2BA52.4B.A22.2B38.A7.
9B2A3B2A6B$33.4B16.4B5.5B2A2B53.A.4B60.A.AB4.2BA6B2A5B2A3B$33.A2BAB
16.4B3.10B54.AB2A2B60.2AB.3B2A8BA6BA3B$35.2A18.4B.4B.6B55.B2A2B62.6B
2A9BA3BA4B$56.7B3.3B.B2A53.3B64.17BA3BA4B$57.5B5.B2.BA.A53.2B66.16B3A
4B$56.3B2AB11.A120.24B$55.4BA4B9.2A118.4B.19B$54.6BA3B2.2A124.4B3.14B
2.B$55.5B2A4B2AB122.4B5.2A10B$56.5B3.4B122.4B5.B2A8B$54.5B5.3B90.R3.
3R3.3R19.4B5.2BA9B$54.2A8.B3A3.B84.2R2.R3.R.R3.R17.4B5.13B$55.A9.2A.A
.B2A84.R2.R3.R.R20.4B5.14B$52.3A12.2A2B2A84.R2.R.R.R.4R16.4B5.15B$52.
A14.2A3B85.R2.R3.R.R3.R14.4B5.4B.10B$68.4B85.R2.R3.R.R3.R13.4B5.2A2B
2.10B$156.3R2.3R3.3R13.4B5.ABAB2.11B$182.4B5.3BA2.11B$181.4B5.4B4.3AB
3AB$180.4B5.4B5.B4A2B$179.4B5.4B6.2B3AB$178.4B5.4B7.3BAB$177.4B5.4B9.
3B$176.4B5.4B$175.4B5.4B$174.4B5.4B$173.4B5.4B$172.ABAB5.4B$171.B2AB
5.4B$170.3BA5.4B$169.4B5.4B$168.4B5.4B$167.4B5.4B$166.4B5.4B$165.4B5.
4B$152.3B9.4B5.4B$151.5B7.4B5.4B$150.6B6.4B5.4B$149.4BA2B5.4B5.4B$
148.4BABAB4.4B5.4B$146.6BABA2B2.4B5.4B$145.8BA2B2.4B5.4B$145.10B2.4B
5.3AB$145.10B.4B5.3BA$144.15B5.3BA$144.14B5.4B$144.13B5.4B$144.12B5.
4B$144.11B5.4B$142.12B5.4B$138.B2.14B3.4B$137.7B2A10B.4B$136.24B$136.
7BA3B2A10B$135.8BA4BA12B$135.13BA12B$135.9BA2BA11B.B2A$135.21B4.BA.A$
134.22B7.A$134.20B9.2A$132.2A19B$127.2A2.A2BA4.14B$124.A2.A3.BABA4.
13B$123.A.A.A.4BA5.9B.B.B2A$124.A2.A.2AB7.8B4.BA.A$127.A.BAB9.3B10.A$
128.A4.A20.2A$129.5A2$131.A$130.A.A$131.A!

Code: Select all

x = 670, y = 281, rule = LifeSuper
102.R3.3R9.R3.3R2.5R4.3R15.R20.3R3.3R8.3R3.3R59.R4.R3.3R9.3R32.R3.3R
5.R9.3R$101.2R2.R3.R7.2R2.R3.R.R7.R3.R9.R3.2R19.R3.R.R3.R6.R3.R.R3.R
57.2R3.2R2.R3.R3.R3.R3.R30.2R2.R3.R3.2R4.R3.R3.R$100.R.R6.R8.R2.R3.R.
R11.R.R.2R4.R4.R19.R3.R5.R6.R3.R.R62.R2.R.R2.R3.R3.R3.R3.R.R.2R26.R2.
R3.R2.R.R4.R3.R3.R.R.2R$99.R2.R4.2R2.5R2.R2.R.R.R2.3R7.R2.2R2.R.5R2.R
20.3R5.R8.3R2.4R59.R.R2.R2.R.R.R.5R2.3R2.2R2.R25.R2.R.R.R.R2.R2.5R2.
3R2.2R2.R$99.5R5.R8.R2.R3.R5.R5.R3.R3.R3.R4.R19.R3.R3.R8.R3.R.R3.R58.
R.5R.R3.R3.R3.R3.R.R3.R25.R2.R3.R.5R3.R3.R3.R.R3.R$102.R2.R3.R8.R2.R
3.R.R3.R4.R4.R3.R3.R4.R19.R3.R2.R9.R3.R.R3.R58.R4.R2.R3.R3.R3.R3.R.R
3.R25.R2.R3.R4.R4.R3.R3.R.R3.R$102.R3.3R8.3R2.3R3.3R4.5R.R3.R7.3R19.
3R2.5R2.R4.3R3.3R58.3R3.R3.3R9.3R2.R3.R24.3R2.3R5.R9.3R2.R3.R$186.R3$
135.2A72.2A61.2A43.2A$134.A.A71.A.A53.A7.A9.A34.3B9.4B$128.2A4.A67.2A
4.A55.3A2.2A.A7.3A32.A3BA9.6B$126.A2.A2.2A.4A61.A2.A2.2A.4A54.A.2BA7.
A35.A4BA7.2BA2BABAB$126.2A.A.A.B.A2.A61.2A.A.A.B.A2.A53.A.2B9.2A35.BA
BA.A6.2ABAB3A3B$129.A.ABABAB66.A.ABABAB55.B3A6.5B37.A.ABAB3.2BA.3B.BA
2B$129.A.AB2AB67.A.AB2AB57.2B5.A4B11.2A27.A4BA2.B2A5BA3B$130.AB.2B69.
AB.2B59.2B3.BA5B10.A29.A3BA.6B.6B$133.3B71.3B57.B2A3BA7B6.2A.A29.3B3.
3BA5B2AB$133.4B6.2A62.4B6.2A49.2A.4BA4B4.A.2B.A31.2A2.3BAB.3B.A2B$
131.3BA2B6.A61.3BA2B6.A41.2A12.B2A3B4.A4BA32.B2.B.3B3ABAB2A$131.3B2AB
3.BA.A61.3B2AB3.BA.A42.A12.5B5.A2B.3AB30.6B.BABA2BA2B$129.10B.B2A60.
10B.B2A43.A.AB2.B5.7B5.A4.2A30.2BA2B4.6B$128.A12B61.A12B46.2AB.3B3.4B
.4B3.2B4.A30.4B2AB5.4B$127.A13B60.A13B48.6B.4B3.4B2.2B5.3A27.3B2A3B$
126.B3A11B59.B3A11B48.10B5.6BAB6.A27.9B$125.4B2.8B60.4B2.8B50.2B2A5B
7.4BABAB31.2AB.8B3.B$124.4B5.5BA59.4B5.6B51.A2BA3B9.3BA2BA30.A.AB2.B
2.9B$123.4B4.6B2AB43.A13.4B4.9B50.BABA4B7.5B2A2B29.A9.8B$108.A13.4B5.
2A4.ABAB42.3A10.4B5.2A4.4B43.A6.BA6B5.10B28.2A10.8B$108.3A10.4B7.A5.
4B44.A8.4B7.A5.4B42.3A5.2B2.4B3.4B.6B41.7B$111.A8.4B5.3A7.4B42.2A7.4B
5.3A7.4B44.A4.2B3.4B.4B3.3B.B2A40.7B6.4B$110.2A7.4B6.A10.4B41.5B3.4B
6.A10.4B42.2A4.B5.7B5.B2.BA.A40.6B4.6B$110.5B3.4B19.4B42.3B2.4B19.4B
41.4B.B2A5.5B12.A40.6B2.BABA2BA2B$112.3B2.BA2B21.4B31.2A7.9B21.4B42.B
2AB2A4.6B12.2A38.10B3ABAB2A$102.2A7.5B2A2B23.4B30.A8.8B23.4B40.A.AB.B
4.4B2A3B.2A43.2A2.2B2A2B.2BAB.3B.A2B$102.A8.6B2A25.4B26.2A.A.B3.10B
25.4B10.2A26.A.AB6.4BA2BA3B2AB41.B2A2B.B2A3.3BA5B2AB$99.2A.A.B3.10B
27.4B10.2A13.A2.3AB.3BA7B26.2B2A9.A27.A10.3BABAB3.2A43.4B.2B4.6B.6B$
99.A2.3AB.3BA7B28.2B2A9.A15.2A2.BA3B2A7B27.BABA10.A24.2A11.3BAB5.2A
42.BA2B2.2B4.B2A5BA3B$100.2A2.BA3B2A7B29.BABA10.A15.AB2A12B21.2A5.A3B
5.5A35.5B6.B2AB40.BABA2.B2AB3.2BA.3B.BA2B$102.AB2A12B23.2A5.A3B5.5A
15.A.2B3.7B.B2A20.A5.4B4.A40.2A9.BA.A40.A2BA3.2A5.2ABAB3A3B$102.A.2B
3.7B.B2A22.A5.4B4.A21.3AB2.7B.BA.A19.A.AB.7B2.B3A38.A7.2AB.A40.A2BA
11.2BA2BABAB$103.3AB2.7B.BA.A21.A.AB.7B2.B3A21.A4.4B5.A20.2AB.7B3.2B.
A34.3A7.A.AB2.3A37.4B12.6B$106.A4.4B5.A22.2AB.7B3.2B.A15.5A5.3BA5.2A
21.12B2ABA34.A9.A7.A37.A2BAB11.4B$101.5A5.3BA5.2A23.12B2ABA15.A10.ABA
B27.7B2A3BAB2.2A41.2A47.2A$101.A10.ABAB29.7B2A3BAB2.2A15.A9.2A2B26.7B
A3B.B3A2.A$103.A9.2A2B28.7BA3B.B3A2.A13.2A10.4B25.10B3.B.A.2A$102.2A
10.4B27.10B3.B.A.2A26.4B23.8B8.A$115.4B25.2A6B8.A30.4B21.9B7.2A$116.
4B23.2B2A5B7.2A31.4B19.4B2.3B$117.4B21.2BAB2.3B42.4B10.A6.4B3.5B$118.
4B19.4B3.5B41.4B7.3A5.4B7.2A$119.4B10.A6.4B7.2A42.4B5.A7.4B8.A$120.4B
7.3A5.4B8.A44.4B4.2A5.4B10.3A$121.4B5.A7.4B10.3A42.9B4.4B13.A$122.BAB
A4.2A5.4B13.A43.6B5.4B$123.B2A6B4.4B58.8B2.4B$124.A5B5.4B57.11B3AB$
124.8B2.4B58.13BA$122.11B3AB59.12BA$122.13BA58.2AB.10B$122.12BA58.A.A
B3.B2A3B$120.2AB.10B59.A6.2BA3B$119.A.AB3.B2A3B60.2A6.4B$119.A6.2BA3B
69.3B$118.2A6.4B72.2B.BA$127.3B71.B2ABA.A$128.2B.BA67.BABABA.A$127.B
2ABA.A64.A2.A.B.A.A.2A$126.BABABA.A64.4A.2A2.A2.A$124.A2.A.B.A.A.2A
65.A4.2A$124.4A.2A2.A2.A63.A.A$128.A4.2A65.2A$126.A.A$126.2A19$.R3.3R
3.3R9.R3.3R3.3R7.R15.R40.R3.3R3.3R11.R62.R3.3R2.5R10.R98.R3.3R3.3R9.
3R2.5R2.3R5.3R15.3R36.3R3.3R3.3R9.3R48.R3.R3.3R9.3R77.3R3.R3.3R9.3R$
2R2.R3.R.R3.R7.2R2.R3.R.R3.R5.2R10.R3.2R39.2R2.R3.R.R3.R3.R5.2R61.2R
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2.R3.R4.R4.R4.R.R2.R.2R92.R2.R3.R.R15.R.R5.R3.R3.R3.R.R.2R4.R7.R38.R.
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$.R2.R.R.R2.4R.5R2.R5.R3.4R3.R2.R2.2R2.R.5R2.R40.R4.2R4.2R2.5R.R2.R2.
2R2.R55.R2.R.R.R4.R2.5R.R2.R2.2R2.R91.R2.R.R.R.4R2.5R4.R3.3R3.3R5.3R
2.2R2.R.5R4.R38.R2.4R2.4R2.5R2.3R2.2R2.R41.R3.R2.R.R.R.5R2.3R2.2R2.R
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3.R3.R3.R.R3.R70.R5.R3.R6.R3.R3.R.R3.R$3R2.3R3.3R8.3R.5R2.3R7.R2.R3.R
7.3R38.3R2.3R3.3R11.R2.R3.R54.3R2.3R4.R12.R2.R3.R90.3R2.3R3.3R8.5R2.
3R3.3R5.3R2.R3.R7.5R34.5R2.3R3.3R9.3R2.R3.R40.3R.3R2.3R9.3R2.R3.R69.
5R.3R.5R8.3R2.R3.R4$8.A98.A86.A121.A99.A74.A100.A$7.A.A96.A.A84.A.A
119.A.A97.A.A72.A.A98.A.A$8.A98.A86.A121.A99.A74.A100.A2$6.5A94.5A82.
5A117.5A95.5A70.5A96.5A$5.A4.A93.A4.A81.A4.A116.A4.A94.A4.A69.A4.A95.
A4.A$4.A.BAB94.A.BAB82.A.BAB117.A.BAB95.A.BAB70.A.BAB96.A.BAB$.A2.A.
2AB91.A2.A.2AB79.A2.A.2AB114.A2.A.2AB92.A2.A.2AB67.A2.A.2AB93.A2.A.2A
B$A.A.A.4BA88.A.A.A.4BA76.A.A.A.4BA111.A.A.A.4BA89.A.A.A.4BA64.A.A.A.
4BA90.A.A.A.4BA$.A2.A3.BABA88.A2.A3.BABA76.A2.A3.BABA111.A2.A3.BABA
89.A2.A3.BABA64.A2.A3.BABA90.A2.A3.BABA$4.2A2.A2BA91.2A2.A2BA79.2A2.A
2BA114.2A2.A2BA92.2A2.A2BA67.2A2.A2BA93.2A2.A2BA$9.2A3B94.2A3B82.2A3B
117.2A3B95.2A3B70.2A3B96.2A3B$11.7B92.7B80.7B115.7B93.7B68.7B94.7B$
11.9B90.9B78.9B113.9B91.9B66.9B92.9B$11.10B89.10B77.10B112.10B90.10B
65.10B81.2BA7.10B$11.11B88.11B76.11B111.11B89.11B64.11B80.2ABA6.3B2A
6B$7.14B85.14B73.14B108.14B86.14B61.14B80.A.3B2.7BAB2A3B$7.14B85.14B
73.14B108.14B86.14B61.14B79.A.A.BA2.6BA4BA2B$6.16B83.16B71.16B106.16B
84.16B59.16B78.A2.A2.7B2A4BA3B$6.17B82.17B70.17B105.17B83.17B58.17B
78.2A4.4B2A6BA4B$6.17B82.17B70.17B105.11B2A4B83.17B58.11B2A4B84.3BA6B
2A5B$7.21B78.21B66.21B101.8BA4BA7B79.21B54.10B2A9B80.3BABA15B$7.24B
75.24B63.24B98.13BA10B76.24B51.24B77.4BAB3A15B$7.25B74.25B62.25B97.
25B75.25B50.11BA13B76.6B2A17B$8.8BABA13B75.8BABA13B63.8BABA13B98.7BA
2BA13B76.8BABA13B51.9B2A13B77.24B$9.7BABA14B75.7BABA14B63.7BABA14B98.
7B3A14B76.7BABA14B51.8BABA13B77.24B$8.8B3A15B73.8B3A15B61.8B3A15B96.
26B74.8B3A15B49.26B75.24BAB$9.26B73.26B61.26B96.26B74.26B49.26B75.23B
A2B$7.29B70.29B58.29B93.29B71.29B46.29B72.25B3AB$7.2A.21B2A4B69.2A.
21B2A4B57.2A.21B2A4B92.2A.21B2A4B70.2A.21B2A4B45.2A.21B2A4B71.2A.12B
2A9B3AB$8.A3.18BA2BA3B70.A3.18BA2BA3B58.A3.18BA2BA3B93.A3.18BA2BA3B
71.A3.18BA2BA3B46.A3.18BA2BA3B72.A3.2BABA5B3A7B3A2B$5.3A5.9B.8B2A4B
67.3A5.9B.8B2A4B55.3A5.9B.8B2A4B90.3A5.9B.8B2A4B68.3A5.9B.8B2A4B43.3A
5.9B.8B2A4B69.3A5.2B2A5B.9B2A3B$5.A7.8B3.4B2.6B68.A7.8B3.4B2.6B56.A7.
8B3.4B2.6B91.A7.8B3.4B2.6B69.A7.8B3.4B2.6B44.A7.8B3.4B2.6B70.A7.2BA5B
3.4B2.2BA3B$15.5B5.4B2.B82.5B5.4B2.B8.A61.5B5.4B2.B105.5B5.4B2.B83.5B
5.4B2.B8.A49.5B5.4B2.B84.5B5.4B2.B$15.6B5.4B84.6B5.4B8.3A61.6B5.4B
107.6B5.4B85.6B5.4B8.3A49.6B5.4B86.6B5.4B$15.7B5.4B83.7B5.4B6.A64.7B
5.4B106.7B5.4B84.7B5.4B6.A52.7B5.4B85.7B5.4B$16.2B.4B5.4B83.2B.4B5.4B
5.2A64.2B.4B5.4B106.2B.4B5.4B84.2B.4B5.4B5.2A52.2B.4B5.4B85.2B.4B5.B
3A$14.4B2.4B5.4B80.4B2.4B5.4B2.4B62.4B2.4B5.4B103.4B2.4B5.4B81.4B2.4B
5.4B2.4B50.4B2.4B5.4B82.4B2.4B5.A3B$14.2A5.4B5.4B79.2A5.4B5.4B.2B64.
2A5.4B5.4B102.2A5.4B5.4B80.2A5.4B5.4B.2B52.2A5.4B5.4B81.2A5.4B5.A3B$
15.A6.4B5.4B79.A6.4B5.7B64.A6.4B5.4B102.A6.4B5.4B80.A6.4B5.7B52.A6.4B
5.4B81.A6.4B5.4B$12.3A8.4B5.4B75.3A8.4B5.6B61.3A8.4B5.4B98.3A8.4B5.4B
76.3A8.4B5.6B49.3A8.4B5.4B77.3A8.4B5.4B$12.A11.4B5.4B74.A8.B2.4B5.5B
61.A11.4B5.4B97.A11.4B5.4B75.A8.B2.4B5.5B49.A11.4B5.4B11.A64.A11.4B5.
4B$25.4B5.4B78.6B2.4B3.8B7.A64.4B5.4B109.4B5.4B79.6B2.4B3.8B7.A52.4B
5.4B8.3A77.4B5.4B$26.4B5.4B76.4B2A8B.9B5.3A65.4B5.4B109.3BA5.4B77.4B
2A8B.9B5.3A53.3BA5.4B6.A81.4B5.4B$27.2BAB5.4B75.3BA2BA18B3.A69.BABA5.
4B109.ABAB5.4B76.3BA2BA18B3.A57.ABAB5.4B5.2A81.4B5.4B$28.2B2A5.4B74.
4B2A21B.2A69.B2AB5.4B109.2A2B5.4B75.4B2A21B.2A57.2A2B5.4B2.4B82.4B5.
4B$29.2A2B5.4B74.29B70.A3B5.4B109.4B5.4B75.29B58.4B5.4B.2B85.4B5.4B$
30.4B5.4B74.26B73.4B5.4B109.4B5.4B75.26B61.4B5.7B85.4B5.4B$31.4B5.4B
74.15B3A8B73.4B5.4B109.4B5.4B75.26B61.4B5.6B86.4B5.4B$32.4B5.2B2A74.
14BABA7B75.4B5.B3A109.4B5.2B2A75.24B60.B2.4B5.5B87.4B5.4B$33.4B5.BABA
74.13BABA8B75.4B5.A3B109.4B5.2A2B75.24B55.6B2.4B3.8B7.A78.4B5.4B$34.
4B5.A3B73.25B75.4B5.A3B109.4B5.BA2B74.25B53.3B3A6BAB.6B2AB5.3A79.4B5.
4B$35.4B5.4B73.24B76.4B5.4B109.4B5.4B74.24B53.3B2A6BABA6B2A3B3.A83.4B
5.4B$36.4B5.4B75.21B77.4B5.4B109.4B5.4B76.9B2A10B53.3B3A7BA8BA4B.2A
83.4B5.4B$37.4B5.4B79.17B77.4B5.4B109.4B5.4B80.4B2A11B53.2BA9BA16B84.
4B5.4B$38.4B5.4B78.17B78.4B5.4B109.4B5.4B79.17B54.B3A22B87.4B5.4B$39.
4B5.4B78.16B79.4B5.4B109.4B5.4B79.16B55.2BA8BA14B87.2BAB5.4B$40.4B5.
4B78.14B81.4B5.4B109.4B5.4B79.14B57.9BA14B89.2B2A5.4B$41.4B5.4B77.14B
82.4B5.4B109.4B5.4B78.14B58.24B89.2A2B5.4B$42.4B5.4B75.11B87.4B5.4B
109.4B5.4B76.11B62.16B3A6B89.4B5.4B$43.4B5.4B75.10B88.4B5.4B109.4B5.
4B76.10B63.24B90.4B5.4B$44.4B5.4B75.9B89.4B5.4B109.4B5.4B76.9B66.11BA
4BA4B91.4B5.4B$45.4B5.4B76.7B90.4B5.4B109.4B5.4B77.7B71.6BA2BAB2A4B
91.4B5.2B2A$46.4B5.4B79.3B2A89.4B5.4B109.4B5.4B80.3B2A69.5B2AB2ABA5B
92.4B5.BABA$47.4B5.4B80.A2BA2.2A85.4B5.4B109.4B5.4B81.A2BA2.2A65.4BA
11B93.4B5.A3B$48.4B5.4B79.ABAB3.A2.A83.4B5.4B109.4B5.4B80.ABAB3.A2.A
63.3BA2BA7B95.4B5.4B$49.4B5.4B79.A4B.A.A.A83.4B5.4B109.4B5.4B11.A68.A
4B.A.A.A62.4BA2BA6B96.4B5.4B11.A$50.4B5.4B80.B2A.A2.A85.4B5.4B109.4B
5.4B8.3A70.B2A.A2.A62.6B2A3B101.4B5.4B8.3A$51.4B5.4B79.BAB.A89.4B5.4B
109.4B5.4B6.A73.BAB.A66.10B102.4B5.4B6.A$52.4B5.4B76.A4.A91.4B5.4B
109.3BA5.4B5.2A70.A4.A68.9B103.4B5.4B5.2A$53.4B5.4B75.5A93.3BA5.4B
109.3BA5.4B2.4B70.5A71.7B104.4B5.4B2.4B$54.3BA5.4B173.3BA5.4B109.3AB
5.4B.2B152.3B2A103.4B5.4B.2B$55.3BA5.4B75.A97.3AB5.4B109.4B5.7B73.A
79.A2BA2.2A99.4B5.7B$56.3AB5.4B73.A.A97.4B5.4B109.4B5.6B72.A.A78.ABAB
3.A2.A97.4B5.6B$57.4B5.4B73.A99.4B5.4B106.B2.4B5.5B73.A80.A4B.A.A.A
94.B2.4B5.5B$58.4B5.4B173.4B5.3BA101.3BA2B2.4B3.5BA2B7.A146.B2A.A2.A
91.6B2.4B3.8B7.A$59.4B5.3BA173.4B5.B2AB99.3B2A9B.5B2A2B5.3A146.BAB.A
93.4B2A8B.9B5.3A$60.4B5.B2AB173.4B5.ABAB98.2B3A7B3A5BABA2B3.A147.A4.A
94.3BA2BA18B3.A$61.4B5.ABAB173.4B5.4B97.B3A9B2A12B.2A146.5A95.4B2A21B
.2A$62.4B5.4B173.4B5.4B97.B3A25B247.29B$63.4B5.4B173.4B5.4B11.A85.2BA
23B150.A99.26B$64.4B5.4B173.4B5.4B8.3A86.BA24B148.A.A99.26B$65.4B5.4B
173.4B5.4B6.A90.24B150.A101.14B3A7B$66.4B5.4B173.4B5.4B5.2A90.24B252.
13BA2BA7B$67.4B5.4B173.4B5.4B2.4B90.17B2A6B251.25B$68.4B5.4B173.4B5.
4B.2B93.15B3ABA4B252.10BA13B$69.4B5.4B173.4B5.7B95.15BABA3B255.7BA4BA
8B$70.4B5.4B173.4B5.6B100.5B2A6BA3B259.4B2A11B$71.4B5.4B170.B2.4B5.5B
100.4BA6B2A4B259.17B$72.4B5.4B165.6B2.4B3.8B7.A91.3BA4B2A6B260.16B$
73.4B5.4B163.4B2A8B.9B5.3A92.2BA4BA6B262.14B$74.4B5.4B162.3BA2BA18B3.
A95.3B2ABA7B262.14B$75.4B5.4B161.4B2A21B.2A93.6B2A3B265.11B$76.4B5.4B
161.29B94.10B266.10B$77.4B5.4B161.26B97.9B267.9B$78.4B5.4B161.15B3A8B
98.7B269.7B$79.4B5.4B161.14BABA7B103.3B2A271.3B2A$80.4B5.4B161.13BABA
8B104.A2BA2.2A268.A2BA2.2A$81.4B5.4B160.25B103.ABAB3.A2.A265.ABAB3.A
2.A$82.BABA5.4B160.24B104.A4B.A.A.A265.A4B.A.A.A$83.B2AB5.4B162.21B
106.B2A.A2.A268.B2A.A2.A$84.A3B5.4B166.17B105.BAB.A271.BAB.A$85.4B5.
4B165.17B103.A4.A270.A4.A$86.4B5.4B165.16B103.5A271.5A$87.4B5.B3A165.
14B$88.4B5.A3B164.14B106.A275.A$89.4B5.A3B162.11B109.A.A273.A.A$90.4B
5.4B162.10B110.A275.A$91.4B5.4B162.9B$92.4B5.4B163.7B$93.4B5.4B166.3B
2A$94.4B5.4B167.A2BA2.2A$95.4B5.4B166.ABAB3.A2.A$96.4B5.4B166.A4B.A.A
.A$97.4B5.4B167.B2A.A2.A$98.4B5.4B166.BAB.A$99.4B5.4B163.A4.A$100.4B
5.4B162.5A$101.4B5.4B$102.4B5.4B162.A$103.4B5.4B160.A.A$104.4B5.4B
160.A$105.4B5.4B$106.4B5.4B$107.4B5.4B$108.4B5.4B$109.3BA5.4B$110.ABA
B5.4B$111.2A2B5.4B$112.4B5.4B$113.4B5.4B$114.4B5.2B2A$115.4B5.2A2B$
116.4B5.BA2B$117.4B5.4B$118.4B5.4B$119.4B5.4B11.A$120.4B5.4B8.3A$121.
4B5.4B6.A$122.4B5.4B5.2A$123.4B5.4B2.4B$124.4B5.4B.2B$125.4B5.7B$126.
4B5.6B$124.B2.4B5.5B$120.6B2.4B3.8B7.A$119.4B2A8B.9B5.3A$119.3BA2BA
18B3.A$119.4B2A21B.2A$120.29B$121.26B$122.15B3A8B$123.14BABA7B$124.
13BABA8B$124.25B$125.24B$128.21B$133.17B$133.17B$134.16B$135.14B$135.
14B$134.11B$135.10B$136.9B$138.7B$142.3B2A$144.A2BA2.2A$144.ABAB3.A2.
A$145.A4B.A.A.A$147.B2A.A2.A$147.BAB.A$145.A4.A$145.5A2$147.A$146.A.A
$147.A!
All explicitly displayed oscillators (in state 1) are in their phase of least population. A period number in state 6 indicates an LCM oscillator, in which case the full-period cells are marked. A period number in state 18 indicates that the smallest oscillator is a multi-signal loop; if the pattern below is in state 13 rather than state 1, it may be constructed explicitly using either snarks (indicated by just the snark heart) or bouncers/bumpers (indicated by the relevant sparker). I stopped at p106 because that is the point where (I think) the rectifier becomes more efficient than the snark for building adjustable glider loops.

Feel free to extend or correct the stamp collection.
Last edited by Freywa on September 10th, 2021, 1:04 pm, edited 7 times in total.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

Sokwe
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Posts: 2238
Joined: July 9th, 2009, 2:44 pm

Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Sokwe » July 3rd, 2021, 8:23 am

That's probably correct up to period 61. I haven't checked much beyond that, but I do see a few issues that need correction:
Freywa wrote:
July 3rd, 2021, 6:26 am
The pipsquirter 2 in the p91 is Scorbie's reduction shown on LifeWiki, but I don't have the reference.
This is smaller (p7 found by Matthias Merzenich, Aug 2014):

Code: Select all

x = 24, y = 25, rule = B3/S23
18b2o$18bo$19bo$16b4o$16bo$18b2o$16bo2bo$16b3o$18bobo$9b3o6bob3o$16b3o
4bo$9bo6bo2bobobo$8b2o8b2ob2o$10bo5bo3bo$7bo8b3obo$7bo3bo7bo$5b2o11bo$
3bo5b3o2b2o2b2o$ob2o4bo5b2o$o3bo3bo$o5bobo3$8b2o$8b2o!
Freywa wrote:
July 3rd, 2021, 6:26 am
For p92 a T-nosed p4 on twin bees shuttle is listed as having 50 cells, but the sum of minimal phases of the component oscillators is 53.
That's because somebody incorrectly changed "twin bees shuttle on 22P4.3" to "twin bees shuttle on T-nosed p4" on the wiki. Here is the 50-cell p46 oscillator:

Code: Select all

x = 14, y = 41, rule = B3/S23
2b2o$2bobobo$4b3o$3bo$2bo4bo$b3obo2bo$bo5b2o$o2bo$bo4$11b2o$11b2o8$4b
3o3b3o$3bo2bo3bo2bo$3b2obo3bob2o16$4b2o5b2o$4b2o5b2o!
A variant of Ivan Fomichev's p92 also has a minimum population of 50, as noted by 2718281828:

Code: Select all

x = 32, y = 34, rule = B3/S23
22b2o5b2o$22b2o5b2o16$21b2obo3bob2o$21bo2bo3bo2bo$22b3o3b3o6$2o14b3o$
2o12bo3bo$13bo4bo$13bo3bo2$13bo3bo$13bo4bo$2o12bo3bo$2o14b3o!
Freywa wrote:
July 3rd, 2021, 6:26 am
The p99 is from here.
This is one cell smaller (the p9 is the monomer form of 68P9):

Code: Select all

x = 24, y = 25, rule = B3/S23
3bo9bo$3b3o5b3o$6bo3bo$5b2o3b2o3$7b3o$6bo3bo$5bo5bo$3ob2o2bo2b2ob3o$ob
ob2o5b2obobo4b2o$b2o2b2o3b2o2b2o4bobo$20bo$19b2o4$16bo$16b2o$11b2obobo
b3o$11bob2obobobo$17bo2b3o$18b2o3bo$20b3o$20bo!
Freywa wrote:
July 3rd, 2021, 6:26 am
Bouncers and bumpers come in handy for periods that are the product of a small number and a prime.
The issue here is that it might not be trivial to construct the smallest form of these oscillators. The shape of the loop needs to be taken into account to make sure that the sparkers and reflector reactions are in low-population phases at the same time.

Edit: This appears to be a list of the smallest known nontrivial oscillators, so I don't think you should include a trivial p34.

Also, if you consider the p51 to be boring (i.e., a least common multiple oscillator), then you should also consider the p26 to be boring.
-Matthias Merzenich

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Freywa
Posts: 862
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 3rd, 2021, 10:57 am

Sokwe wrote:
July 3rd, 2021, 8:23 am
That's probably correct up to period 61. I haven't checked much beyond that, but I do see a few issues that need correction:
The first post has been updated with the smaller oscillators and auxiliary information.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Freywa
Posts: 862
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:

Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 5th, 2021, 5:50 am

May be the smallest-known p132 (I've indicated it as such on LifeWiki's oscillator page):

Code: Select all

x = 30, y = 24, rule = B3/S23
bo4b2o$obo2bobo$bo4bo4$6bobo7bo$5bo2bo6b3o$3bo3b2o3bo2bo2bo$2bo2bo4bo
2bo3b3o$2bo6b2o9b2o$8b2o3bo3bo$12bo3bo3b2o$8b2o9b2o6bo$10b3o3bo2bo4bo
2bo$3b2o6bo2bo2bo3b2o3bo$2bo2bo6b3o6bo2bo$2bobobo6bo7bobo$3bo2bo$7bo$
4bobo$23bo4bo$22bobo2bobo$22b2o4bo!
Edit: A two-glider rectifier loop achieves 116 cells for all periods 133 + 4n (4n+1, n >= 0; periods 109 to 129 require ten gliders and 156 cells). Three gliders give all periods of the form 110 + 8n, five give 106 + 8n (collectively 4n + 2; can be improved to one glider at periods >= 266) and six give 107 + 4n (4n + 3) in 136 cells.

Code: Select all

x = 224, y = 100, rule = LifeHistory
66.A148.A$65.A.A146.A.A$.D3.3D3.3D11.D40.A148.A$2D2.D3.D.D3.D3.D5.2D$
.D6.D5.D3.D4.D.D2.D.2D32.5A144.5A$.D4.2D4.2D2.5D.D2.D2.2D2.D9.2A20.A
4.A121.2A20.A4.A$.D6.D5.D3.D3.5D.D3.D10.A23.A2.A121.A23.A2.A$.D2.D3.D
.D3.D3.D6.D2.D3.D10.A.A21.2A.A2.A118.A.A21.2A.A2.A$3D2.3D3.3D11.D2.D
3.D11.2A18.A5.A.A.A118.2A18.A5.A.A.A$63.A.A4.A2.A138.A.A4.A2.A$63.A2.
A2.2A141.A2.A2.2A$64.2A147.2A$.D3.D3.3D21.2A147.2A$2D2.2D2.D3.D21.A
148.A$.D3.D2.D25.A.A146.A.A$.D3.D2.4D23.2A12.A134.2A$.D3.D2.D3.D35.2A
147.3A$.D3.D2.D3.D34.A149.A$3D.3D2.3D36.2A147.3A$30.A18.A$29.A.A$29.A
.A$30.A2$123.D3.3D2.5D10.D$122.2D2.D3.D5.D3.D5.2D$123.D2.D3.D4.D4.D4.
D.D2.D.2D$123.D2.D.D.D4.D2.5D.D2.D2.2D2.D$123.D2.D3.D3.D5.D3.5D.D3.D
24.A$123.D2.D3.D3.D5.D6.D2.D3.D22.2A$44.A77.3D2.3D4.D12.D2.D3.D23.2A
13.A$43.A.A146.A.A$43.A.A146.A.A$25.A18.A148.A$25.2A96.D3.3D3.3D$27.A
94.2D2.D3.D.D3.D$25.2A96.D6.D.D$25.A12.2A83.D4.2D2.4D$38.A.A82.D6.D.D
3.D$40.A82.D2.D3.D.D3.D$40.2A80.3D2.3D3.3D$9.2A$4.2A2.A2.A161.2A$.A2.
A4.A.A160.A.A$A.A.A5.A18.2A143.A$.A2.A.2A21.A.A$4.A2.A23.A$5.A4.A20.
2A$6.5A2$8.A$7.A.A$8.A3$151.A$151.A.A$151.2A9$132.A$131.A.A$131.A.A$
132.A13.2A$147.2A$146.A10$126.3A$128.A$126.3A$140.2A$140.A.A$142.A$
142.2A$111.2A$106.2A2.A2.A$103.A2.A4.A.A$102.A.A.A5.A18.2A$103.A2.A.
2A21.A.A$106.A2.A23.A$107.A4.A20.2A$108.5A2$110.A$109.A.A$110.A!
I wrote the following program to determine the exact minimum populations:

Code: Select all

#!/usr/bin/env python3
from itertools import product
import lifelib
sess = lifelib.load_rules("b3s23")
lt = sess.lifetree(n_layers=1)

rectifier = lt.pattern("""x = 34, y = 42, rule = B3/S23
8bo$7bobo$8bo2$6b5o$5bo4bo$4bo2bo$bo2bob2o$obobo5bo$bo2bo4bobo$4b2o2bo
2bo$9b2o9$17b2o$17b2o8$7b2o22b2o$8bo21bo2bo$5b3o23b2o$5bo6$14b2o$15bo$
12b3o$12bo!""")
rectifier2 = rectifier("rot180", 52, 74)
glider = lt.pattern("bo$2o$obo")(17, 23)

def construct_rectifier_loop(p):
    if p%4 == 0 or p < 106:
        raise ValueError
    n_gliders = [10,5,6,0,10,3,6][p%8-1]
    if n_gliders == 5 and p >= 266:
        n_gliders = 1
    if n_gliders == 10 and p >= 133:
        n_gliders = 2
    exts = (p*n_gliders - 266) // 8
    pat = rectifier + rectifier2(exts, exts)
    for _ in range(n_gliders):
        pat = (pat+glider)[p]
    return pat

for (prange, desc) in ((range(109, 300, 4), "4n+1"), (range(106, 300, 8), "8n+2"), (range(110, 300, 8), "8n+6"), (range(107, 300, 4), "4n+3")):
    popdict = {}
    for p in prange:
        pat = construct_rectifier_loop(p)
        popdict[p] = min(pat[i].population for i in range(p))
    print(desc + ":")
    for (k, v) in popdict.items():
        print(k, v)

Code: Select all

4n+1:
109–129 156
133+ 116
8n+2:
106 169
114 166
122 164
130 166
138 166
146 163
154 159
162 159
170 159
178 148
186 142
194 137
202 135
210–258 133
266+ 113
8n+6:
110 156
118 154
126 156
134 156
142 154
150 151
158 149
166 151
174 143
182 134
190 130
198 126
206+ 123
4n+3:
107+ 136
As an example, the p486 R-heptomino hassler is beaten by this three-glider rectifier loop at 123 cells:

Code: Select all

x = 202, y = 224, rule = B3/S23
8bo$7bobo$8bo2$6b5o$5bo4bo$4bo2bo$bo2bob2o$obobo5bo$bo2bo4bobo$4b2o2bo
2bo$9b2o13$16bobo$16bobo$16b3o3$7b2o22b2o$8bo21bo2bo$5b3o23b2o$5bo6$
14b2o$15bo$12b3o$12bo97$124bo$125bo$123b3o3$138bo$137b2o$137bobo37$
189bo$187b3o$186bo$186b2o6$196bo$169b2o23b3o$168bo2bo21bo$169b2o22b2o
8$183b2o$183b2o9$191b2o$190bo2bo2b2o$190bobo4bo2bo$191bo5bobobo$194b2o
bo2bo$194bo2bo$191bo4bo$191b5o2$193bo$192bobo$193bo!
140 + 8n (8n + 4) periods are achievable in 141 cells using the p4 bumper:

Code: Select all

x = 35, y = 35, rule = B3/S23
14b2o$6bo7bo9bo$6b3o3bobo7b3o$9bo2b2o7bo$8bobo10b2o$9b2o$9b2o6bo14b2o$
10b2o4bobo13bo$10b2o3bo2bo11bobo$10b2o4b2o11bobo$b2o22b2ob2o$2bo22b2o$
2bobo26b2o$3b2o26bo$32b3o$27bo6bo$7b2o15bob2o$6bo2bo14b2o$7bobo$o7bo$
3o$3bo26b2o$2b2o4bo21bobo$3b3o3bo22bo$4bo4bo22b2o$3bo4bo8b2o4b2o$2bob
2o10bo2bo3b2o$2bo13bobo$b2o14bo$23b3o$12b2o12bo$13bo7bo3bo$10b3o7bob2o
2b3o$10bo9bo7bo$19b2o!
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

User avatar
calcyman
Posts: 2601
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by calcyman » July 5th, 2021, 5:17 pm

What do you do with ill crystallographers? Take them to the mono-clinic!

hotdogPi
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 5th, 2021, 5:20 pm

What about the multiples of 15 where there are various pentadecathlon glider shuttles?

EDIT:
90+24n (114 shown): 92

Code: Select all

x = 31, y = 25, rule = B3/S23
7b2o4bo$7b2o3bobo$13bo3$2o2b2o$2o2b2o19bo$25b3o$22bo5bo$22b6obo$3b2o
22bobo$2bo2b2o15b2o2bo2b2o$2bo4b2o13bobo2b2o$2o3bob2o17bobo$bobo23bo$b
ob6o11bo$2bo5bo9bobo$3b3o13b2o$5bo19b2o2b2o$25b2o2b2o3$17bo$16bobo3b2o
$17bo4b2o!
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Sokwe » July 5th, 2021, 7:42 pm

A bit off-topic, but it would also be nice to collect the oldest known oscillator for each period. For example, every period above 60 was known in October 1996 using Herschel loops; every multiple of 4, 6, or 10 above period-100 was known in 1994 using traffic jams; etc.

Edit: I started a topic for discussing the first known oscillators for each period here.
-Matthias Merzenich

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 5th, 2021, 8:08 pm

All periods 104 + 16n (112 + 16n) are achievable in 120 (121) cells using two adjacent pairs of bouncers and bumpers, which therefore covers the last remaining periods:

Code: Select all

x = 35, y = 36, rule = B3/S23
10bo2$8bob3o$10b2obo8bo$10bob2o6b3o$11b3obo3bo$19b2o$13bo$17bo13b2o$16b
obo12b3o$17b2o2b2o2b2o2bo2bobo$21b2o2b2o2b2o2b2o$29b2o2$2b2o5b2o$3bo5b
2o$3bobo19bo$4b2o18bobo$8b2o14bo2bo$7bobo15b2o$8bo2$4b2o23b2o$2bob2o23b
obo$bo15b2o12bo$4bo12bo13b2o$2obo15bo4b2o$2o16bo5b2o$18bo2$12b2o9b2o$
13bo9b2obo$10b3o13bo$10bo15bo$23bo2bo$24b2o!

Code: Select all

x = 37, y = 37, rule = B3/S23
12bo$11bobo$10bo3bo$11bo3bo8bo$12bo3bo5b3o$13bo3bo3bo$14bobo4b2o$15bo
$19bo$18bobo7bo2b2o$19b2o2b2o2bo3b2o2b2o$23b2o2bo7b2o$28b4o3$3b2o5b2o
$4bo5b2o15bo$4bobo19bobo$5b2o19bo2bo$9b2o16b2o$8bobo$9bo$5bo25b2o$31b
obo$3b3obo25bo$2bob2o12b2o13b2o$2b2obo12bobo$ob3o20b2o$19b2o4b2o$2bo15b
o2$13b2o9b2obo$14bo10bobo$11b3o12bo$11bo13b2o$25b2o$25b2o!
Hence for all periods at least 187 there exists an oscillator with minimum population at most 141.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

hotdogPi
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 6th, 2021, 9:55 am

116 isn't covered.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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calcyman
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by calcyman » July 6th, 2021, 12:16 pm

hotdogPi wrote:
July 6th, 2021, 9:55 am
116 isn't covered.
Yes, it's mentioned in this post that it can be done (in 105 cells). viewtopic.php?f=7&t=2036&start=2325#p118405
What do you do with ill crystallographers? Take them to the mono-clinic!

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 6th, 2021, 12:19 pm

hotdogPi wrote:
July 6th, 2021, 9:55 am
116 isn't covered.
Of course it wasn't until I decided to put three gliders in the p4 bumper loop:

Code: Select all

x = 61, y = 61, rule = B3/S23
20b2o$12bo7bo9bo$12b3o3bobo7b3o$15bob3o7bo$14bob2o9b2o$14bo2bo$23b
o$22bobo$15bo2bo2bo2bo$16b2o4b2o2$24b2o$24bobo$24bo3$b2o$2bo$2bobo
$3b2o3$7b2o$6bo2bo$7bobo$o7bo$3o55b2o$3bo54bo$2bo53bobo$2bo2bo2b2o
44b2obo$5bo2b2o41b6o$3bobo45b3o$2bobo16bo35b2o$2bo19bo34bo$b2o17b
3o35b3o$52bo7bo$51bobo$51bo2bo$47b2o3b2o$48b2o$47bo$56b2o$56bobo$
58bo$58b2o7$37b2o4b2o$36bo2bo3b2o$36bobo$37bo6bo$44b2o$32b2o12bo$
33bo7b2o2bo$30b3o7bobo3b3o$30bo9bo7bo$39b2o!
The smallest known oscillators for all periods where a non-trivial oscillator is known can now be automatically generated through my new Skopje program (Skopje being the capital of North Macedonia). The above oscillator was generated through the following code:

Code: Select all

from shinjuku.skopje import skop
print(skop(116)[0].rle_string())
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

hotdogPi
Posts: 1017
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 6th, 2021, 12:37 pm

About your new program: I thought there were pentadecathlon shuttles for all sufficiently high multiples of 15, not just 60, 75, or 90 mod 120.

Here's an example that's 45 mod 120:

Code: Select all

x = 52, y = 50, rule = B3/S23
15b3o$15bobo$15b3o$15b3o$15b3o$15b3o$15bobo$15b3o5$2bo6bo$b2o6b2o$3o6b
3o$b2o6b2o$2bo6bo15$32bo4bo2b2o4b2o2bo$31b2o3bo3b3o2b3o3bo$31bobo3bo2b
2o4b2o2bo3$32b3o2$31bo3bo$31bo3bo2$32b3o3$32b3o2$31bo3bo$31bo3bo2$32b
3o!
0 mod 120:

Code: Select all

x = 60, y = 66, rule = B3/S23
11b2o$11b2o8$11b3o$10bo3bo$9bo5bo$9b2obob2o4$14bo$8o7b2o$ob4obo6b2o$8o
27$52b8o$52bob4obo$52b8o$46b2o4$44b2obob2o$44bo5bo$45bo3bo$46b3o8$47b
2o$47b2o!
30 mod 120:

Code: Select all

x = 41, y = 64, rule = B3/S23
b3o2$o3bo$o3bo2$b3o3$b3o2$o3bo$o3bo2$b3o8$15bo2b2o4b2o2bo$14bo3b3o2b3o
3bo$15bo2b2o4b2o2bo7$21b2o$19bobobo$17bobobo$18b2o7$12bo2b2o4b2o2bo$
11bo3b3o2b3o3bo$12bo2b2o4b2o2bo8$37b3o2$36bo3bo$36bo3bo2$37b3o3$37b3o
2$36bo3bo$36bo3bo2$37b3o!
15 mod 120:

Code: Select all

x = 80, y = 46, rule = B3/S23
39b2o$39b2o$15b2o3bo2bo3b2o22b2o3bo2bo3b2o$15b5o4b5o22b5o4b5o$15b2o3bo
2bo3b2o22b2o3bo2bo3b2o4$33b3o8b3o$35bo8bo$34bo10bo4$39b2o$39b2o11$b2o
6b2o58b2o6b2o$o2bo4bo2bo56bo2bo4bo2bo$o2bo4bo2bo56bo2bo4bo2bo$o2bo4bo
2bo56bo2bo4bo2bo$b2o6b2o58b2o6b2o2$18b3o38b3o$18b3o38b3o$19bo40bo$19bo
40bo$19bo40bo$18bobo38bobo3$18bobo38bobo$19bo40bo$19bo40bo$19bo40bo$
18b3o38b3o$18b3o38b3o!
This leaves only 105 mod 120.

Also, 138+184n

Code: Select all

x = 56, y = 58, rule = B3/S23
2o9bob2o$2o3b2o3bo2b2o2b3o12b2o$5b2o3bo6b2o13b2o$10b2o3b3o$12bo3bo2$
12bo3bo$10b2o3b3o$10bo6b2o13b2o$10bo2b2o2b3o12b2o$11bob2o29$42bo$43b2o
$42b2o4$39b3o$39bo$27bob2o9bo$21b2o3bo2b2o2b3o17bo$21b2o3bo6b2o17bob2o
$26b2o3b3o19b2o$28bo3bo20bo2$28bo3bo$26b2o3b3o$21b2o3bo6b2o13b2o$21b2o
3bo2b2o2b3o12b2o3b2o$27bob2o22b2o!
184+92n

Code: Select all

x = 69, y = 69, rule = B3/S23
3bo5b2o$2b3o4b2o$b2ob2o2$obobobo2$b2ob2o$b2ob2o$3bo9$b2obo3bob2o$bo2bo
3bo2bo$2b3o3b3o8$9b2o$9b2o29$28bo21b2o$29b2o9b2o7bobo15b2o$28b2o10b2o
7bo17b2o$49b3o2$64bo$61b2o3bo$49b3o9b2obob2o$49bo10bo6b2o$49bobo9b2obo
b2o$50b2o9b2o3bo$64bo!
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 6th, 2021, 2:08 pm

hotdogPi wrote:
July 6th, 2021, 12:37 pm
184+92n
It's actually 184+184n, but all those shuttles have been added.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 8th, 2021, 5:44 am

The p5 variant of the p6 thumb shuttle achieves 130 + 40n in 119 cells – the base version even beats the p130 shuttle – but by this point only produces new SKOP130, SKOP170 and SKOP250. Can a smaller sparker be used?

Code: Select all

x = 39, y = 27, rule = B3/S23
10b2o4bo$10b2o3bobo$16bo3$3b2o2b2o2b2o15b2o3b2o$3b2o2b2o2bobo14b2o3b2o
$11bo2$24b2o2b3ob3o2b2o$24bo2bo7bo2bo$6b3o16bobo7bobo$5bobobo16bo4bo4b
o$3b3o3b3o15b3o3b3o$2bo4bo4bo16bobobo$bobo7bobo16b3o$o2bo7bo2bo$2o2b3o
b3o2b2o3$4b2o3b2o19b2o2b2o$4b2o3b2o19b2o2b2o3$22bo$21bobo3b2o$22bo4b2o
!
Edit: SKOP130 is now 55P10 on Beluchenko's p13 at 89 cells:

Code: Select all

x = 27, y = 27, rule = B3/S23
6bo$5bobo$5bobo$ob2obob2o$2obobo3bo$5b4o$4bo2bo$4b3o$7bo$4b4o$3bo11bo
$4b4o6bobo$7bo$4b3o9bo$4bo2bo5bo2bo$5b4o8bo$2obobo3bo7bo$ob2obob2o4bo
3bo$5bobo6b3o$5bobo2b2o7b3o$6bo3b2o6bo3b2obo$18bo7bo$18bo6bo$19bo2bo2$
16b2o$16b2o!
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

hotdogPi
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 8th, 2021, 8:40 am

Is there a way to put low-period sparkers (and mid-period such as Merzenich's p31 and Beluchenko's p40) in the program, test ones with LCM equal to the number specified, and keep as a candidate any ones that are non-trivial and don't get destroyed?

Also looking for a 105 mod 120 with six or fewer pentadecathlons, since we have all the rest of the multiples of 15. I don't know of any, but I imagine something must exist.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 8th, 2021, 9:12 am

hotdogPi wrote:
July 8th, 2021, 8:40 am
Is there a way to put low-period sparkers (and mid-period such as Merzenich's p31 and Beluchenko's p40) in the program, test ones with LCM equal to the number specified, and keep as a candidate any ones that are non-trivial and don't get destroyed?

Also looking for a 105 mod 120 with six or fewer pentadecathlons, since we have all the rest of the multiples of 15. I don't know of any, but I imagine something must exist.
It would be fairly easy to write another program to generate LCM oscillators (perhaps using some of the code in Nakano) but since I only care about the absolute smallest oscillators - and the loop bound is very tight - it would be better to add LCM oscillators to Skopje by hand.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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iNoMed
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by iNoMed » July 9th, 2021, 7:19 am

This may not be an adjustable glider loop (As is typical of the oscillators in this thread), but I've got a new SKOP25 for the collection:

Code: Select all

x = 21, y = 22, rule = B3/S23
18bo$b2o13b3o$o2bo2b2o7bo$b2o2bobo7b2o$3b2o$3bo$2obo9bo$o2bob2o5b2o4b
2o$2b2obo7bo4b2o4$2b2obo7bo$o2bob2o5b2o$2obo9bo$3bo13b2o$3b2o12bobo$b
2o2bobo11bo$o2bo2b2o2b2o7b2o$b2o8bo$5bob4o$5b2obo!
This slightly-trivial (in terms of discovery difficulty, not in terms of a lack of cells oscillating at period-25) period-25 pre-pulsar shuttle variant has a minimum population of just 83 cells, five less than the previous SKOP25's minimum of 88 cells. :)

Code: Select all

x = 35, y = 5, rule = B3/S23
4b2o3b2o3bo3b2ob2o3b2ob2o$2o2bobo3bo2bobobobobobobobobobo$obobo2bo2bob
o2bobo2bo2bobo3bobo$2bobo3bobobobo2bo5bobo3bobob2o$b2ob2o3b2ob2o3b2o3b
2ob2o3b2ob2o!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 9th, 2021, 9:32 am

Freywa wrote:
July 8th, 2021, 9:12 am
It would be fairly easy to write another program to generate LCM oscillators (perhaps using some of the code in Nakano) but since I only care about the absolute smallest oscillators - and the loop bound is very tight - it would be better to add LCM oscillators to Skopje by hand.
Anything that adds up to under 100, or even slightly over 100, should be smaller than glider loops as long as it works.
1 cell spark on leading row/column
p3 caterer: 12
p3 jam: 13
p4 mold: 12
p4 mazing: 12
22P4: 22
T-nosed p4 variant: 25
p5 pseudo-barberpole: 15
p5 pipsquirter: 41
p6 unix: 18
p6 thumb: 27
Jason's p6: 28
T-nosed p6: 40
37P7.1: 37
38P7.2: 38
p8 blocker (also obo): 15
p8 Kok's galaxy (also obbo): 28
p9 thumb 1: 36
37P10.1: 37
55P10: 55
p11 rattlesnake: 33
Beluchenko's p13: 34
66P13: 66
34P14 shuttle: 34
p15 pentadecathlon: 12
Rob's p16: 21
Rich's p16: 34
Jason's p22: 36
48P9: 48
p29 pre-pulsar shuttle: 54
p30 queen bee shuttle: 20
Merzenich's p31 (dupolet): 48
Jason's p33: 60
p46 twin bees shuttle: 28
p54 shuttle: 48
Merzenich's p64: 34

Domino spark
20P4: 20
p4 heavyweight emulator: 34
p5 fumarole: 18
Jason's p6: 28
44P7.2: 44
p8 figure eight: 12
24P10: 24
p14 tumbler: 16
p15 pentadecathlon: 12
Merzenich's p31 (domino): 48
68P32: 68
Jason's p33: 60
Beluchenko's p40: 26
p54 shuttle: 48
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 10th, 2021, 12:18 pm

Skopje is now in its own repository here. I've added the missing half of the 184+92n cases as well.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 11th, 2021, 11:14 pm

Better construction for p30+120n (51 cells) using buckaroos:

Code: Select all

x = 37, y = 27, rule = B3/S23
o$3o$3bo$2b2o$9b2o20b2o$5bo2b2o21b2o$4bobo3bo$3bo3bo$3b5o23bo$2b2o
3b2o21bobo$3b5o21bo3bo$4b3o22b5o$5bo22b2o3b2o$29b5o$30b3o$31bo6$4b
2o$4b2o$33b2o$33bo$34b3o$36bo!
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 13th, 2021, 12:54 am

For most periods of the form 8n+4 starting from p412 attaching a mold to the rectifier loop of half the period yields new SKOPs of 125 or 135 cells:

Code: Select all

x = 98, y = 119, rule = B3/S23
9bo$8bobo$9bo2$7b5o$6bo4bo$5bo2bo$2bo2bob2o$bobobo5bo$2bo2bo4bobo$5b2o
2bo2bo$10b2o3$2bobo$5bo$bo2bo$obobo$o2bo$b2o6$16b2ob2o$17bobo$18bo2$8b
2o22b2o$9bo21bo2bo$6b3o23b2o$6bo6$15b2o$16bo$13b3o$13bo28$54bobo$55b2o
$55bo2$68b2o$68bobo$68bo2$85bo$83b3o$82bo$82b2o6$92bo$65b2o23b3o$64bo
2bo21bo$65b2o22b2o8$79b2o$79b2o9$87b2o$86bo2bo2b2o$86bobo4bo2bo$87bo5b
obobo$90b2obo2bo$90bo2bo$87bo4bo$87b5o2$89bo$88bobo$89bo!
Yes, if I've got to combine LCM and loop constructions to get new SKOPs, I'll do it.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Sokwe » July 13th, 2021, 7:32 pm

New smallest p96 oscillator ("p96 honey farm shuttle", 63 cells) discovered by David Raucci:

Code: Select all

x = 22, y = 32, rule = B3/S23
2b2o$2b2obo$6bo$3bo$4bob2o$6b2o11b2o$19b2o2$20bo$19bobo$18bo2bo$17bo2b
o2$10b2o5bo2bo$9bo2bo6b2o$10b2o$12bo$b2o8bo$bo2bo6bo2$bo2bo$o2bo$obo$b
o2$b2o$b2o11b2o$14b2obo$18bo$15bo$16bob2o$18b2o!
-Matthias Merzenich

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Freywa
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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 15th, 2021, 10:10 pm

Is snacker on 34P14 shuttle SKOP126 at 74 cells? (I couldn't get thumb 1 on 34P14 shuttle to work.)

Code: Select all

x = 20, y = 26, rule = B3/S23
8bo$7bo2bo$4b2o5bo$3bo8bo3b2o$3bo8bo3b2o$4bob2ob3o$8b2o2$8b2o$4bob2ob
3o$3bo8bo3b2o$3bo8bo3b2o$4b2o5bo$7bo2bo$8bo$2o16b2o$bo7b2o7bo$bobo3bo
4bo3bobo$2b2o2bo6bo2b2o$5bo8bo$5bo8bo$5bo8bo$2b2o2bo6bo2b2o$bobo3bo4bo
3bobo$bo7b2o7bo$2o16b2o!
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by Freywa » July 16th, 2021, 12:33 am

I've found (and committed into Skopje) a better 90+120n pentadecathlon shuttle at 61 cells:

Code: Select all

x = 28, y = 22, rule = B3/S23
7b2o4bo9bo$7b2o3bobo8bo$13bo8bobo$23bo$23bo$2o2b2o17bo$2o2b2o17bo$12bo
9bobo$13bo9bo$11b3o9bo3$4bo$4bo$3bobo$4bo17b2o2b2o$4bo17b2o2b2o$4bo$4b
o$3bobo8bo$4bo8bobo3b2o$4bo9bo4b2o!
In particular this gives a tied SKOP90 that I've christened as Silverstream.

Edit: 98+56n in 105 cells yielding a new SKOP98 called Gallus:

Code: Select all

x = 39, y = 23, rule = B3/S23
12b2o4bo$12b2o3bobo12b2o$18bo5b2o5bob2o2b2o$24b2o5bobo3b2o$31bo$5b2o2b
2o18bo$5b2o2b2o5bo$14bobo12bo$15b2o14bo$24b2o5bobo3b2o$24b2o5bob2o2b2o
$8b2o22b2o$2o5bob2o2b2o$2o5bobo3b2o$7bo$5bo$28b2o2b2o$5bo22b2o2b2o$7bo
$2o5bobo3b2o$2o5bob2o2b2o5bo$8b2o9bobo3b2o$20bo4b2o!
Edit 2: Better constructions for 0, 15 and 45 mod 120:

Code: Select all

x = 168, y = 52, rule = LifeHistory
134.A$134.A$16.3A55.3A56.3A$15.A3.A53.A3.A$15.A3.A53.A3.A$16.3A55.3A
56.3A$134.A$134.A$134.A$134.A$16.3A14.3D38.3A15.D2.5D33.3A19.D2.5D$
15.A3.A12.D3.D36.A3.A13.2D2.D58.2D2.D$15.A3.A12.D3.D36.A3.A14.D2.D57.
D.D2.D$16.3A13.D.D.D37.3A15.D3.3D34.3A16.D2.D3.3D$32.D3.D55.D6.D34.A
17.5D5.D$32.D3.D55.D2.D3.D34.A20.D2.D3.D$33.3D55.3D2.3D56.D3.3D$2A3.A
2.A3.2A44.2A3.A2.A3.2A45.2A3.A2.A3.2A$5A4.5A44.5A4.5A45.5A4.5A$2A3.A
2.A3.2A.3A40.2A3.A2.A3.2A.3A41.2A3.A2.A3.2A.3A$15.A57.A58.A$16.A57.A
58.A7$98.2A$32.2A3.A2.A3.2A50.A4.A$32.5A4.5A49.A6.A$32.2A3.A2.A3.2A
48.A8.A$94.A8.A$94.A8.A$95.A6.A54.2A6.2A$27.3A58.A7.A4.A54.A2.A4.A2.A
$26.A3.A57.A9.2A56.A2.A4.A2.A$26.A3.A125.A2.A4.A2.A$27.3A58.A68.2A6.
2A$87.A.A2$87.3A$151.A$27.3A121.A$26.A3.A56.3A60.A.A$26.A3.A120.A$27.
3A57.A.A61.A$88.A62.A$151.A$88.A61.A.A$88.A62.A$151.A!
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Re: Smallest Known Oscillators to p106 (and Beyond)

Post by hotdogPi » July 16th, 2021, 9:29 am

Boat-bits:

240: 46, although there's probably a LCM that beats it somewhere

Code: Select all

x = 33, y = 47, rule = B3/S23
4b2o$5bo$4bo$4b2o13$6bo$2o3bo3b3o$2o2bo6bo$5bo5bo$6b2ob2o5$27b2o$27b2o
2$24b2o5b2o$24b2o5b2o$18bo$16bobo$17b2o11$27b2o$28bo$27bo$27b2o!
368: 50

Code: Select all

x = 35, y = 40, rule = B3/S23
19bo$17b3o$16bo$16b2o$30bo$28b3o$27bo$27b2o9$2b2o$bobo$bo$2o11b3o17b2o
$12bo2bo18bo$12b2o2bo16bo$15b2o16b2o5$6b2o$5bobo$5bo$4b2o6$17b2o$18bo$
17bo$17b2o!
492: 87

Code: Select all

x = 44, y = 38, rule = B3/S23
34bo$34b3o$32b2o3bo$31bobob2obo$32bobobobo$36bob2o$33bo2bo$34bobo$33b
2ob2o2$2o$bo20b2o$bobo16b2o3bo$2b2o21bo15b2o$19bo5bo15bo$20bo3bo14bobo
$21b3o15b2o7$29b2o$29b2o$22b2o$21bo$22b2o$42b2o$43bo$5b4o33bo$4bo4bo
32b2o$3bobo3bo$2bobo3bo$2bo$2bo$2bo2bo$3b2o!
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉟,㊱,㊳S,㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,70,72,74S,75,76S,80,84,90,96,100,102S,108,110,112,114G,116,117G,120,126G,128,138,147,154,156,180,196S,217,486,576

S: SKOP
G: gun

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