Morse-Thue sequences are obtained by simply counting numbers. Each
number is converted to a specific base (ie.- binary, octal, decimal, hexadecimal,
etc.) and the sum of its digits is calculated. The resulting sequence is
the Morse-Thue sequence. It is not exactly a fractal set but it has many
of their properties, as self-similarity and endless complexity.
A Morse-Thue sequence depends on three parameters, all of them positive integers (except the start parameter which can also be zero). The algorithm counts from the start parameter, using a given step. Then converts the resulting numbers into any base.
Here's an example of a Morse-Thue sequence: first we count in steps
of 3, starting from 10:
| 10 | 13 | 16 | 19 | 22 | 25 | 28 | 31 | 34 | 37 |
Then we convert the numbers to another base. In this example we choose
base 8:
| 12 | 15 | 20 | 23 | 26 | 31 | 34 | 37 | 42 | 45 |
Finally, we take the sum of the digits of each number in the sequence:
| 3 | 6 | 2 | 5 | 8 | 4 | 7 | 10 | 6 | 9 |
And that's it! In this example, the above sequence would be the resulting
microsequence.