I played around with a related problem - find the shortest string containing every binary number of length n. There are 2^n substrings, and I seem to recall bei

I played around with a related problem - find the shortest string containing every binary number of length n. There are 2^n substrings, and I seem to recall being able to to do it in 2^n + n - 1 bits. In other words, perfect overlap was possible at least up to n=10. I was interested in this because it's an optimal way to plot Julia sets by running the iteration backward and choosing one or the other square root. To visit all parts of the outline you'd want to apply every sequence of root selection (positive or negative) up to some length. Doing it at random is cool, but for a fixed number of points you want one of these sequences.