Fourier, entropy of junk DNA

Googling for this, returned some close matches and it is reasonable to assume that if the DNA is not compressible that it contains information, the easy, and perhaps wrong, answer. It also seems that information which is complex and repetitive would represent some type of wave on wave action that would be amenable to Fourier. It probably would be projected against several other functions that are themselves convolved.

There is some doubt on my part that a sequence that is easily compressible is actually without information. Physical systems are not integer systems and they are also 4 dimensional. An example might be wrapping a string with regularly spaced dots around a bumpy coffee can to reveal that a picture is formed. It does seem that a regular pattern, on irregular space can contain information and that is making me wonder if it really is true that compressible information is without meaning, when taken out of context. The continuous and subtle variation in bond strength of GC and AT pairs could just as well be the information measure and by simply saying that it contains no information because it can be compressed to n*(GACT) would likely not be valid.

My conclusion is that, the assumption that compressible data contains no information, is only valid in a limited context. Physical systems are continuously variable in 3 space and do not have the same unit time, binary state-wise restriction. I might guess now, that a regularly repeating pattern in a very irregular world is information because it is a difference to what would arise naturally and requires energy and work to exist.

ADDED: A good example of this would be an image interleaved on some number which would seem to be random to the eye, but if a regular repeating mask was applied to that, it would reveal a comprehensible form. The regular pattern could certainly be compressed , but in this context it would contain a great deal of information because of its association with a second set. Biological entities are required to perform work to create DNA and as such it would seem that from a naive perspective that it implies some purpose in the construction.