An infinite sequence of 0s and 1s, defined in any of the following (equivalent) ways. In each case, an obvious "limit" exists (and can be made rigorous), which is the Morse sequence
- Write down a 0. Then, at each stage, copy the previous stage's word, then copy it "inverted", switching 0's and 1's.
- Define a morphism by
0 → 01
1 → 10
and extend it to words; now repeatedly apply it to the word "0".
In each case, the same sequence is obtained:
0
01
0110
01101001
0110100110010110
...
This sequence is aperiodic, but still strongly recurrent.
Method 2 above is an example of an L-system which converges to a single limit.