Solved that, spending the whole day. Thank you for your explanation. I really liked your morse katas!

Haven't completed all the tests yet. I'm using kmeans2 from scipy package and almost every test is quite good. I've noticed the noise in the last test only after I actually printed the input sting. As I understood from this discussion (am I correct?), the sequances like "...0000000010000..." or "...111110011111111..." are noisy (these short inclusions is noise - not the dot). (*)

(if (*) is correct) Basically, in the description to the kate there are no words about noise so the solutions should treat every inclusion of 0's or 1's as some characters for the output. If it is so, you should include the warning about the noise to the description or get rid of it in the last test, because a correct solution which is related to the original description won't work with the last test.

Default tests are incorrect. Change closing brackets.

Won't work if given argument is not None but it still isn't a Node object.
Your code will work successfully with

get_nth(1, 0)