First applet: Given a full word w, a positive integer p,
and a non-negative integer d, this implementation outputs a d-valid,
p-periodic partial word
contained in w if any such word exists. A d-valid partial
word is one that has no two holes
within distance d.
Second applet: Given a morphism and a seed string that determine a fixed point,
together with a non-negative integer n, this implementation outputs the list of
all length n factors of this fixed point.
Usage: Morphisms are inputted by specifying the alphabet (as a list with no delimiter)
in the "alphabet" field and the images of these letters (as a space-delimited list in the corresponding order)
in the "images" field. The morphism defined by a→bc, b→bd,
c→ca, d→cb is provided as an example.
There are several restrictions on the morphism and seed: The morphism must be such that the image of
each letter has length at least 2. Furthermore, the seed must be a prefix of its image.
(This ensures that with repeated application of the morphism to the seed, the word grows exponentially and
converges to a fixed point.)
Tip: If your morphism maps some letter to a word of length less than 2, try raising
the morphism to a higher power, since this new morphism will generate the same fixed point.
For example, consider the morphism defined by a→abc, b→ac,
c→b. The square of this morphism is defined by
a→abcacb, b→abcb, c→ac,
which sends every letter to a word of length at least 2.
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| Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No.
DMS-0754154. The Department of Defense is also gratefully acknowledged. |
| Disclaimer: Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. |
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