I wonder if analogous continuous objects can exist. For instance, can there be a continuous function on the circle R/Z f : R/Z —> R and some fixed L > 0, such that f contains all continuous functions g : [0, L] —> R as represented on an arc [c, c+L] ⊂ R/Z of the circle, via g(x) = f(x+c) (addition modulo 1) ??? Or something along these lines, maybe for a restricted class of functions f and g ? —Dan Adam Goucher wrote: ----- de Bruijn sequences Veit Elser wrote: ----- Is there a name for cyclic sequences (necklaces) of length 2^n that contain all the integers 0, … , 2^n-1 expressed in binary in the 2^n subsequences of length n? For example, for n=4 the sequence 0000100110101111 contains 0, 1, 2, 4, 9, 3, 6, 13, 10, 5, 11, 7, 15, 14, 12, 8. ----- -----