the first ten characters are, as far as I know, arbitrary, but the following ten are the first ten plus one dot. Then the rest of the alphabet is the first ten plus two dots
Ah, see I assumed there was 'some' pattern. Its interesting that it doesn't seem more deliberate. Why groups of 10 for 26 letters? Maybe the random pattern at the beginning is for better differentiation of symbols?
It seems to me that it was designed with children in mind. Get them to memorize the first 10 letters of the alphabet (one for each finger) with drills. After that, it's easy to repeat the pattern for the next 10, and the last 6 are a breeze. I expect it would work equally well for alphabets with different numbers of characters.