I’m trying to make a map with many islands/small continent/like things, and I want to make an infinite ocean that is optimized well. I do not want to use terrain because of poor optimization. How would I do this? (using gerstner waves)
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If 3D waves are what you would like to achieve, I would recommend making an infinite Baseplate with a mesh (examples of these can be found in the Toolbox), and designing wave models and sizing them differently. These waves could be moved across the map at different locations and speeds.
I definitely wouldn’t use Terrain from experience of distance-based quality levels. Hope this helps! 
How would I make the waves move?
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Using CFrame would be the easiest option, although for more lifelike effects you could use PrismaticConstraints to change speeds a little easier.
This is definitely something to look at, just know that it’s very costly on performance.
It actually might be a better idea to use an EditableMesh ocean. If you add some optimization and such it should be quite performant and also seem essentially infinite.
Have been working on one but just need to implement some gerstner waves rather than the perlin I was using, and it’s quite performant (tested on low-end specs).