Write down a 0:
0
Now mentally “flip” this string in binary, exchanging 0s and 1s, and append this new string to the existing one:
0 1
Keep this up and you’ll get a growing string of 0s and 1s:
0 1 1 0
0 1 1 0 1 0 0 1
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0
…
This is the Thue–Morse sequence, named after two of its discoverers, Axel Thue and Marston Morse.
One interesting property of the sequence is that, no matter how far it’s extended, it contains no “cubes,” no instances in which some nonempty string occurs three times in a row. For…The post An End in Sight appeared first on FeedBox.