For pretty much every villain in the show, we know their motives. For example, Chrysalis had to feed her hive, Nightmare Moon was jealous, and Starlight had lost a childhood friend. Even with Sombra, one of the least explored villains in the show, we got a backstory in the comics. But we know nothing about Discord's backstory or motives. And while it's never specifically stated, I've begun to guess as to why Discord turned the world into his own personal playground of chaos. The first explanation is because he thought it was fun, which does hold up fairly well, but I have an idea of what a second reason could be. My explanation is that he did it because if he didn't, he very likely would have died. In Discordant Harmony, we see that Discord is a being of pure chaos, and will fade away without it. That's why he did everything he did. He needed that chaos to survive. That's why he's constantly stirring up trouble. To keep himself alive. And while you might say that he could have created his chaos the way he does now, I have an explanation for that too. In the episode, we see that Discord loses his powers without chaos. So perhaps, the more chaos there is, the more power he gains. This also makes sense when you consider the fact that Discord toned down his chaos after his reformation. He realized that there was more to his life than his power, and so, he saw no reason to go to those extremes. And when Tirek came around, he was too tempted and reverted to his old ways. Once again, he was reminded that there was more to life than power, and was redeemed once more.
What to do you think? I personally think this would be an interesting story idea, but there might be some holes.

So, for me, Discordant Harmony was a huge continuity error. While it's humor was great, I see a major flaw.

Let me explain a few reasons:
1. He was encased in stone for over 1000 years, unable to cause his own chaos. But even if ponies had provided any chaos, it wouldn't have been enough to sustain him, and the fact that he was in the Canterlot Gardens doesn't put him near any chaotic disputes or anything. He would have ceased had we followed Discordant Harmony.
2. Tirek Sapped him of all magic he possessed. If that had happened and the rules of Discordant Harmony applied, he would have once again, ceased to exist.
3. Even if his realm of Chaos was the source of his chaos magic gathering, wouldn't he have ceased having been trapped in stone for over 1000 years.

Those are just some examples. I could go into more detail of why I see Discordant Harmony as a huge continuity error. As to his motives, well, I'd say that Discord spread his chaos, because he simply was bored with a Harmonious Equestria. Kind of like a, "They're evil for the sake of just being evil" if you will.

Discord's motive is boredom.

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Just for the sake of friendly debate, to your points.
#1 While he was in stone in Canterlot, you'd have to agree that being in the city with most of Equestria's nobles, he was sustained by their constant beliefs of being better than the masses, and their back stabbing of one anither, as Starlights proven, even ponies are capable of evil. Another possible sorce would be the fact a good few unicorn nobles are tribalist and xenophobic, so any non-ponies or even earth and pegasi ponies are looked down upon.
#2 While Tirek did sap the magic of ponies and Discord, the elements of harmony showed they still had magic inside of themselves, he just sapped their current magic, over time they would have replenished their magic reserves. Case and point Twilight has exhausted her magic before, and her physical self, but later she looks fine.
#3 Truth is Discord may have been in both places at once, and was bidding his time. He shows he can make multiple copies of himself, personally i believe he didnt even get put in stone, but allowed himself to be stationary as he was because Discord is like Celestia, he was shaping her future and path to fit the world and the timelines needs.

On the idea of why discord did and does what he does, is evident ( he is therefore he does. ) They are called the elements of harmony, Discord most likely made them to balance himself, to keep everything going the way it should, chaos, evil/dark must exist for harmony, good/light to exist.

1. Acting chaotic is more than enough to sustain him. Discord doesn't need to use his powers to stay alive, in fact it wasn't the lack of chaos that was destroying him, it was him acting completely normal, which I guess created a paradox since he is chaos?

2. Nope, yet again he doesn't need chaos magic to sustain himself, he just needs to keep his personality.

3. Not sure how to answer this. I guess fra?

As for the OP, basically what everyone else said: He was bored. I personally think he did want a friend, but the ponies acted like dickheads because he looked weird. Just look at their reactions to him in that very episode; they don't hate him but they sure as hell think he is a freak.

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As for the fact he was encased in stone, I see this as a way of time freezing. Think about it, if we assume Discord ages, he would have aged while he was in stone. As with Tirek, well, you got me there.

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Discord is the Spirit of Disharmony, following that logic he should have ceased to exist the moment he became friends with somebody.

But anyway, in the episode he was dying not because he wasn't just keeping his chaos under control like he always has to do, but because he was metaphorically (and literally) destroying all that made him chaotic and umpredicable to be what he thought Fluttershy wanted him to be; and all that made him chaotic just happened to be his whole self.

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It wasn't just to survive. He'd stay alive by just being himself, but what I'm saying is that the more chaos there is surrounding him, the stronger his power grows.