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These patterns almost follow the same rules I was looking at yesterday but they are second-order 🔗. Which means instead of only looking at the previous generation to generate the next generation (row), you look at the previous two generations; The neighbours from x - 1 and the state of the cell to perform the rules on from x - 2

Rule 18 (Second Order) - Random Starting Row
Rule 22 (Second Order) - Random Starting Row
Rule 25 (Second Order) - Random Starting Row
Rule 37 (Second Order) - Random Starting Row
Rule 54 (Second Order) - Random Starting Row