Hans Zantema: Morphic sequences: characterization, visualization and equality


Event Details


Morphic sequences form a natural class of infinite sequences, most times defined by fixed points of morphisms. They cover well-known examples like the Thue- Morse sequence and the Fibonacci sequence.
In this talk we focus on the following three aspects of morphic sequences:
1. Equivalent characterizations of the class of morphic sequences. These include characterizations based on automata and by finiteness of a particular class of subsequences.
2. Visualization by turtle graphics. Criteria have been developed resulting in either finite turtle figures with a lot of symmetry, or turtle figures with fractal patterns. Playing around with examples satisfying these criteria yield a wide range of amazing figures, each generated by a computer program of just a few lines.
3. Proving that different representations define the same morphic sequence.
Surprisingly, exploiting a suitable criterion in many cases this can be done fully automatically by a simple computer program. This yields elementary induction proofs, however being quite complex by distinguishing several cases, while checking by hand is not needed as they are correct by construction.