A hypothesis about rises and falls

Recently I've been reading about Islamic history. It's a topic about which I admit to knowing little, owing to a personal bias favoring classical and Western European history. The period during which Islam flourished, from the 7th century to the 13th, I know as the Dark Ages. How's that for a bias?

The book's author, I suspect, shared a similar bias. I suspect this because the chapters covering the Islamic side of things from the 7th century to the 13th century comprise about 200 pages, whereas the European side of things during the same time period, supposedly a dark age, is covered in three times as many pages. And to be clear, I'm not even halfway through those 200 pages about Islamic history. I write this to make it clear how much of a novice I am with Islamic history.

And yet, I'm already struck by an interesting realization about the rise and fall of progressive Islamic civilization: it was actually the rise and fall of two distinct Islamic civilizations. I'm not referring to the individualistic tribes or provinces of Islamic civilization; rather, I'm specifically referring firstly to the Arabian expansion, starting in the early 7th century shortly after Mohammed's death and lasting until the early 11th century, and secondly to the Turkish conquest of Persia and much of what the Arabs had conquered. Both the Arabian expansion and the Turkish conquest were carried out in the faith of Islam---indeed, the Turks' invasion seemed to strengthen the declining faith of the Arabs---so it's convenient to join the two into a single entity called Islamic civilization, but a more nuanced understanding of this period entails two distinct civilizations (or sub-civilizations), each with their own ascent and descent.

There's a specific reason why I find this interesting. The Arabian expansion, which exploded into Persia, northern Africa, Spain, eastern Europe, and southern Asia, was done with exceptional speed. It took the Arabs fewer than two hundred years to conquer a larger amount of territory than the Romans ever managed in their thousand years of dominance. Then, about another two centuries later, Persia was invaded by the Turks, many of the remote Islamic provinces declared independence in all affairs but religious matters, and Arabia was left much to itself after having given the world a new major religion.

The Turks conquered swiftly as well, reaching their zenith after a hundred years or so before their decline became the decline of Islamic civilization itself (and the terminal decline of Islamic progressiveness) by the end of the 13th century. To recap: Arabs ascended for about 200 years and descended for about 200 years; Turks ascended for about 100 years and descended for about 100 years.

This fits a pattern that I've observed studying the millennia-long narrative of civilizations rising and falling: that is, civilizations tend to spend about the same amount of time declining as they do growing. The faster a civilization grows, the faster it dies. This is probably best exemplified by the conquests of Alexander, who in the span of fewer than two decades created one of the ancient world's largest-ever empires, only to have that empire permanently torn apart by his very successors upon his death. Conversely, take the case of Rome, which slowly over half a millennium build a complex, self-preserving empire that took roughly the remainder of that millennium to crumble back into the chaos out of which it emerged.

What do you guys think? Can you think of some counterexamples to this pattern?