01356/34/8

[c0b0p0]

While searching for interesting Generations rules, this rule caught my eye. While soup searching I found this 3-cell O(log n) growth pattern.

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O.O
...
.O.

Based on this, one can construct arbitrarily long period oscillators.

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x = 40, y = 40, rule = 01356/34/8
17.A$19.A$17.A15$A.A2$.A$38.A2$37.A.A15$22.A$20.A$22.A!

... and a spaceship:

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x = 7, y = 3, rule = 01356/34/8
2.A.A$2A4.A$2.A.A!

[Lewis]

Another way of creating oscillators, this time using only one of the infinite growth patterns instead of 4:

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x = 60, y = 7, rule = 01356/34/8
A2$27.EFGA$.A2.A2.A.A2.A.A.A.A.A3.A.ADAG.FGA.A.A.A3.A.A.A.A.A.A2.A.A$
27.EFGA2$59.A!

Also, the 3-cell pattern itself still grows infinitely in a similar way if the rule is changed to 01356/34/4.

[c0b0p0]

Here is a clean three-glider synthesis of the O(log n) growth pattern. If a rake is found, a "breeder" with growth rate O(n log n) will be proven possible.

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x = 36, y = 3, rule = 01356/34/8
2.A.A12.A.A11.A.A$2A4.A8.A4.2A7.A4.2A$2.A.A12.A.A11.A.A!