Thue–Morse sequence
Okay kiddo, so have you ever played with a pattern of colors? Like say, blue-red-blue-red and then it keeps repeating? That's kind of like what the Thue-Morse sequence is.
You can make this sequence by starting with just one letter, say "0". Then you add it's "opposite", which is "1". So now you have "01".
Next, you take the existing sequence ("01") and flip all the letters to get their opposites. In this case, "01" becomes "10". Then you add this new sequence to the end of the original one, creating "0110".
You then repeat this process over and over again, each time adding a flipped sequence to the end of the current sequence. It kind of looks like a pattern of black and white squares.
But what's interesting is that you can actually use this sequence to help solve math problems, like finding patterns in numbers or studying shapes. It's like a little math puzzle that can help us figure out how things work. Pretty cool, right?
You can make this sequence by starting with just one letter, say "0". Then you add it's "opposite", which is "1". So now you have "01".
Next, you take the existing sequence ("01") and flip all the letters to get their opposites. In this case, "01" becomes "10". Then you add this new sequence to the end of the original one, creating "0110".
You then repeat this process over and over again, each time adding a flipped sequence to the end of the current sequence. It kind of looks like a pattern of black and white squares.
But what's interesting is that you can actually use this sequence to help solve math problems, like finding patterns in numbers or studying shapes. It's like a little math puzzle that can help us figure out how things work. Pretty cool, right?