Does this help a bit?

Some. Though it is still couched in a lot of terms that aren't immediately descriptive to the layman.

Is this close to a paraphrase of the problem?

A motif is a subsequence, of initially unknown length, that repeats, with minor variations, several times within a localised region of a (gene) sequence.

The problem of finding them is that of recognising that there are several near repetitions of a subsequence within a (relatively) short stretch (100s or low thousands) of 'letters'.

If that is close, then a few questions arise:

• Is the 'source material' for the search coded in terms of just {acgt}?

  Or are the encoded in that other form where 1 letter is used to specif: this position might be any of 'a' or 'c'; or this position might be any of 'a' or 'g' or 't'?

• Is there a minimum length to a motif?
• Will the repetitions be the same length?
• Will the seeker normally have a rough location from (or around) which to start looking?

Maybe I've nothing to contribute to the problem; but I was playing with a novel indexing algorithm a couple of years that might lend itself to this problem. My problem is getting a clear understanding of the problem in terms I can relate to without having to go off and become conversant in the genomic terminology.