The New Persian Empire
Sometimes, my brain decides that it wants to hold a particular image of things. This is normal and most people's brains do the same thing. What concerns me is when my brain decides to have a concrete image of something in the future. That's what happened in the case of New Persia.
Today, what remains of the Persian Empire is the nation of Iran. The empire itself was more or less a thing from about 550 b.c.e. With a few minor breaks for invaders who disrupted everybody (Mongol hoards, for example). Their last emperor, referred to in the West as the Shah, was deposed in the late seventies and dies in exile.
There is still an exile government called the National Council of Iran. Their main goal is to overthrow the actual sitting government of Iran. That doesn't seem to be going too well, and I wouldn't expect too much from it.
The actual current government of Iran is an Islamic theocracy. Though they are fairly harsh from a western point of view, they aren't as radical and wildly destructive as groups like the Islamic State. However, the Iranian government does not get on well with western powers, particularly the United States. It seems that when the Iranians got rid of the Shah, who was pretty much a dictator, the U. S. and the British helped put him back in power and he promptly dealt with all the people who overthrew him. When they kicked the Shah out a second time, they captured the American embassy, leading to what we call the Iran Hostage Crisis.
Today, we still don't get along with Iran. To the West, the Iranian government are fundamentalist whackos who want nuclear weapons. The the people in charge of the current Iranian government, the Americans are a bunch of degenerates who destroy, kill, and corrupt anybody and everybody. Sure, there are citizens in both countries who are more moderate ("discomfort to the infidels!"), but the official positions are hostile to each other.
As much as we may dislike the government of Iran, we have to admit that Iran is one of the more stable countries in the middle east. This could have something to do with the fact that a huge majority are Shia Muslims and all other religions add up to a tiny minority. Also, the culture is strongly influenced by the long-standing Persian culture and less by the more tribal Arabic culture found neighboring countries.
Back to my imaginings, though, and I see a time in a century or so where Iran has expanded to encompass more of the old Persian Empire. I see their borders extended westward to take in almost all of Iraq (leaving a sliver of the north to the Kurds who would be too much trouble to fight). I also see that border taking a chunk out of the east side of Saudi Arabia, and maybe a little sliver out of the southern border of Turkey.
How could this happen? Why would the U. S. and its allies allow such a thing? I'm not sure yet. I have a few guesses, but that's all they are. There are two major points that affect the American response.
First, if Iraq becomes more unstable it would be reasonable that the Shia people there would ask for assistance from their Shia neighbors in Iran. Much like Russia's recent annexation of Crimea, this would give Iran a reason to march into Iraq to protect "their people" living there and then choose to stay. If the result was a sudden increase in stability in the region, it would be hard to argue against it and Iran's borders would be permanently stretched.
Help from the Dragon
It has already been seen that China been extending its reach into the Middle East, coming in through Pakistan and wanting partnerships further in. It would be easy to see them backing Iranian expansion. If nothing else, this would irk the U. S., but, more importantly, it gives them better access to Middle Eastern oil reserves. The American government may be willing to push back against Iran, but doesn't want to pick a fight with China at this time.
The second thing I see happening is a reduction in interest from European countries. Many countries in Europe have pinned their hopes on renewable energy sources with less pollution. They don't want to rely on oil for anything. More importantly, they don't want to have to deal with refugees from the Middle East. Anything that keeps the peace where the refugees come from will be somewhat welcome. If Iran is involved in stabilizing the region, even through expansion of its borders, many Europeans will see that as a good thing. The English may be the exception, but they are sort of responsible for a lot of the turmoil there in the first place.
Help from the Bear
The third thing involves Russia. Russia likes to annoy the Americans easily as much as the Chinese, if not more. They also tend to be more comfortable with dictatorships and harsher forms of government. We see that now in Syria where Russia has sided with the dictator instead of the rebels fighting him. Note that the U. S. is on the side of the rebels. If there is an agreement for the Russians and Iranians to fight the Islamic State, the Americans won't be in a position to do much about it. That hard-line coalition can move into the Islamic State held areas, set up a "peace keeping" force and just settle in. The Russians, with memories of Afghanistan, would probably be willing to let Iran have the real control of the area.
If Russia really wants to be sure of its welcome in the Middle East, they just have to come down in favor of a Palestinian State. If they say the current nation of Israel was created by the British Empire and other western countries (over guilt about the actions of the Nazis), they are basically saying Israel is not a valid nation. The rest of the Middle East will welcome the Russians with open arms.
If these things come to pass, the borders of Iran would expand as described above. Over time, I also see their hardline regime being mellowed by the practicalities of actual life. They will still be an Islamic theocracy for the next couple of centuries, but what that means may change with so many people to rule. They will have to adapt to interacting with the rest of the world, starting with Russia and China. As their isolation crumbles, some of their cultural defenses will crumble too. As we saw with the Soviet Union, you can get more change with blue jeans and burgers than you can with ballistic missiles.
The Romans learned early on that conquered peoples have to have a path to becoming full members of your society. When the new Persia opens up schools that teach the Persian language (as spoken in Iran) instead of Arabic, the culture will change, but change can happen in lots of ways. Their own culture will have to make small concessions to be be more open and inclusive. If not, their new empire may not last more than three centuries.
So, that's the image in my head. That's what I see as a stabilizing occurrence in the Middle East. That's what I foretell about the New Persian Empire.