The Turks were not fleeing from the Mongols. Most of them joined them, as they were similar people, especially the nomadic Turks. Some conquered the Mongols, (Timur) and others were already in Anatolia. The Turks in Anatolia didn't look much like the the Turks in Central Asia. They were more mixed with the local Grecian and Arab people.
At their height they were far more advanced. Yeah they went backwards later but so do all civs at their end. The Brits weren't very expansionist after WW2 but they still had alot of their empire left.
The Ottomans could have been militaristic/ expansionist, or really any of the traits, but these two were picked for balancing purposes.
But you are incorrect my man, back in the middle ages 1100's, 1200's the ottoman empire had the best scientists in the world.
The Ottomans came to power in the 1300's and reached their height in the 1500's. The Seljuk Turks, their predescors were ruling earlier.
So its safe to say, the Ottomans, and the 3.000 troops that came from Turkmenistan, conquered Asia minor.
BUt the Ottomans were already in the Anatolia. Osman, Hourse of Osman was in Anatolia and they had been there for a while. If you look at a historical map from 1000 to 1500 you'll see what was going on the ME during that time period.
Ok, here's a summary. Brief and doesn't cover most things. Its from the top of my head. Whatver:
Around 800 AD, we have Abbasid Caliphate ruling Arabian Peninsula, Syria, Iraq, Persia, Afghanistan, Egypt and a bit more of northern Africa and into modern day Uzbekistan/ Turmekistan. They are Arabs. There, that is the Arab empire everybody ask's about. A very large one, I think it was larger than the Roman empire. They are centered in Baghdad. The Turks are happily living in modern day Khazikistan and around the Caspian sea.
1000 AD: The Abbasi's collapse. Persia returns to its native dynasties, Egypt, Syria become independent also. Abbasids are finished off by the Persians. The Fatamid dynasty takes control of Egypt. The Ghuzz Turks in modern day Afghanistan and Turmekistan are convereted to Islam. The Seljuk Turks are taken as slave soldiers to defend Baghdad from the Persians. They win, and then rebel agaisnt the Abbasids, finally finishing them off. Then they go and conquer Persia, Iraq, Palestine, and into Anatolia but are defeated at Constantinople. Crusaders arrive later and conquer back Palestine and bits of Anatolia. The Turks also destroy the Fatamid dynasty in Egypt. But the Egyptain governor, a kurd, Saladin, takes over Egypt and makes it the Ayyubid dynasty. Later the Mamlukes, also Turks, conquer Egypt and end the short lived Ayyubid dynasty. The Seljuks split into several kingdoms. The Rums in anatolia and the Great Seljuk Sultanate in Persia and Central Asia.
Then our friend Chingis/ Genghis Khan shows up destroys all the empires in the area and most of the cities along with it. The Rums recover though and aren't too affected by the Mongol conquest.
1200's. The Ilk Khanate rules over Persia and Turmekistan. The Seljuk Rum dynasty is cornered between Byzatine and Ilk Khanate. The Mamlukes take control of Egypt. The Chagtai have central Asia, and the Golden Horde is in Russia.
1400's. Timur takes control of the Chagtai's. They are mix of Mongols and Turks, mostly Turks. He leads them and conquers Persia, Iraq, northern India, and central Asia. At the same time the Ottomans come to power in Anatolia and cross into the Balkans and conquer there and take all of Anatolia except Constantinople. They are sieging the city, when Timur starts conquering which results in a war between Timur and the Ottomans, which Timur wins. But the Ottomans are only hindered a bit and continue expanding. Timur's empire collapses, and returns to the little Turkish states.
At this time, there is really no major power in the world. Europeans are still relatively backwards, and made up of small states and kingdoms other than the Holy Roman empire. Ottomans are unrivaled. The Mamlukes are a threat but then destroyed and conquered. The Safavids are also somewhat destroyed and weakened.
The Ottomans were most likely a noble family (House of Osman) from the Seljuk Rum's times, and managed to survive the Mongol onslaught.
For a few centuries the Ottomans were unrivaled.
Also a side note: Its interesting that around Timur's time and a bit later, most of Asia was ruled by Turkish/Mongoloid peoples. Central Asia, Mongolia, China, Persia, Egypt, India (not the Mughals, there was a few other Delhi sultanates, mostly destroyed by Timur) and Anatolia.
My summary is not totally correct but it is mostly. I did a report on the Seljuks a few years ago, and although now I can't rememeber most of their names, there was alot going on then.