I'll preface this by saying that Islamic art and architecture are not specialties of mine. And that this question is made difficult particularly because we are talking about a style that is evident from (to my knowledge) at least the 8th century Ummayads (of which the "Winter Palace" originally located in what is now Jordan and now at the Pergamon Museum in Berlin is a really lovely example.) and remains a feature of most traditional forms of traditionally "Islamic" art practices down to this day (e.g. the tiling of Sultan Qaboos Mosque in Oman, or the patterning of Turkish kilim rugs [this one being quite similar to the one under my feet as I type this now :)

The sheer volume and spread of such patterns in Islamic art across the virtually the entirety of the greater Islamic world from Morocco to western China defies easy categorization. As the Encyclopaedia of Islam entry on "Arabesque" notes:

From [the 11th century] on it occurs throughout the Islamic world in countless variations, so that it is impossible to classify the various forms according to a chronological order or according to a national or dynastic predilections.

While the sheer volume of this cultural output I think we generally say defies specific symbolism (e.g., I'm not aware of anything quite so explicit as the supposed interlocking of an H (for Henri II) with two Cs (for Catherine de Medici) supposedly forming two Ds (for Henri's mistress Diane de Poitiers)) in Islamic art).

That's not to say this style is without meaning. For one thing, the adoption of aniconism (that is, the refusal to depict humans) is itself a religious and in all likelihood a political statement that seems to have become characteristic of Islam in about the 8th century (notably, we can point to the coinage reforms of Abdul Malik in circa 696CE as a decisive removal of human images and introduction of calligraphy--itself distinctive of Islamic art).

Other aniconic symbols also have some specific meanings, for example the association of peacocks with heaven, or of peacocks, lions, elephants and certain other animals with royalty.

One of the other problems in answering your question, however, is the passive phrasing of "was there symbolism attached to different patterns." This raises the issue of "by whom?" and "when?"

This takes us down a sort of art and literary criticism/interpretation hole that I'm not really qualified at all to answer, but the answer to this is going to much more limited if, for example, we mean symbolism attached by the original artist at the time, given that such surviving artworks are generally anonymous, at least until the modern era.

We might then get into the level of specificity that we can attach to the symbolism of particular features. For example, in about the 11th century Muqarnas designs spread rapidly across the Islamic world and become an almost stereotypical feature of transitional arches, vaults, domes, squinches, etc. in mosques and other religious buildings.

Now, I think we can safely assume that aesthetically if not also religiously the application of this feature to transitional spaces in architecture had some meaning. But in reading various interpretations of what that meaning was my own personal BS detector starts to go off. For example, in this article, arguing not from any text but rather from the form itself, the author interprets muqarnases as being a manifestation of Islam's understanding of the universe as atomistic. I think much more solidly, the author of that piece quotes another historian who cites actual poetic references to the meaning of the structures themselves as being "Domes of Heaven."

More broadly, there is quite a lot of interesting discussion to be had about the potential religious symbolism of particular patterns, or of the use of complex patterns in general. For example, might such patterns have been aesthetically pleasing to a religious tradition that is traditionally open to highly repetitive, rhythmic, even trance-inducing forms of worship? That seems highly plausible to me.

Again, I don't claim that this is definitive, and scholars have written about the specific meaning of particular geometric works in greater detail. But in general, aside from the sources referenced above you might want to read further:

"Art and Mithal: Reading Geometry as Visual Commentary" in Iranian Studies by Carol Bier.

The entries on "Architecture" and "Muqarnas" in the Encyclopaedia of Islam.