Fascinating. As a child, I also detested praise, and I have always had something bordering on an obsession for symmetry and an aversion to asymmetry.
I hadn’t heard of the Thue-Morse sequence until now, but it is quite similar to a sequence I came up with as a child and have tapped out (0 for left hand/foot/leg, 1 for right hand/foot/leg) or silently hummed (or just thought) whenever I was bored or was nervous.
[commas and brackets added to make the pattern obvious]
As a kid, I would routinely get the pattern up into the thousands as I passed the time imagining sounds or lights very quickly going off on either the left (0) or right (1) side.
Every finite subsequence of your sequence is also a subsequence of the Thue-Morse sequence and vice versa. So in a sense, each is a shifted version of the other; it’s just that they’re shifted infinitely much in a way that’s difficult to define.
Fascinating. As a child, I also detested praise, and I have always had something bordering on an obsession for symmetry and an aversion to asymmetry.
I hadn’t heard of the Thue-Morse sequence until now, but it is quite similar to a sequence I came up with as a child and have tapped out (0 for left hand/foot/leg, 1 for right hand/foot/leg) or silently hummed (or just thought) whenever I was bored or was nervous.
My sequence is:
[0, 1, 1, 0] [1001, 0110, 0110, 1001] [0110 1001 1001 0110, 1001 0110 0110 1001, 1001 0110 0110 1001, 0110 1001 1001 0110] …
[commas and brackets added to make the pattern obvious]
As a kid, I would routinely get the pattern up into the thousands as I passed the time imagining sounds or lights very quickly going off on either the left (0) or right (1) side.
Every finite subsequence of your sequence is also a subsequence of the Thue-Morse sequence and vice versa. So in a sense, each is a shifted version of the other; it’s just that they’re shifted infinitely much in a way that’s difficult to define.