What does this pic mean?(guess it's a binary number)

Question

This number was presented in yesterday class and explained by teacher that they were lined up according to a certain rule. I think we'll use nibbles to solve this. I also think that the circle means something like pi or a clock (but not sure).

Answer 1

This is in fact a de Bruijn sequence: every four-bit word appears exactly once in the circle.

Answer 2

Start a sequence with $$ 1,1,1,1$$ and then repeatedly append the smallest choice $a_n\in\{0,1\}$ such that the $(a_{n-3},a_{n-2},a_{n-1},a_n)$ does not equal any previous $(a_{k-3},a_{k-2},a_{k-1},a_k)$. This will make you continue the sequence as follows $$ 1,1,1,1,0,0,0,0,1,0,0,1,1,0,1,0,1,1,1$$ at which point you have to stop, but also have completed the circle (with overlap). As a consequence, every quadruple $(x,y,z,u)\in\{0,1\}^4$ occurs exactly once in the circle.