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Aug 17, 2016 at 8:04 history edited elias CC BY-SA 3.0
added 402 characters in body
Aug 17, 2016 at 7:53 comment added elias Sorry if my solution was not clear. I suggested building one 2-row-pattern of the first kind, then below it the other one. I will include a picture for better understanding. As the two patterns don't share a common tetromino, you can put these different $2\times\mathbb Z$ patterns below each other with arbitrary horizontal translation without same types of tetrominoes touching.
Aug 17, 2016 at 6:53 history answered elias CC BY-SA 3.0