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So I'm looking to implement the diamond square with the ability to step through the generation and not having it all generated at once. Something like in this video: https://www.youtube.com/watch?v=9HJKrctqIJI

What's the best method for implementing the terrain such that I can control the subdivisions? I was looking at QuadTrees but I wasn't sure if they would be the best approach.

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By definition the diamond-square algorithm is an iterative algorithm, so there is nothing preventing you from pausing it between two steps.

What do you mean by controlling the subdivision ? Only subdivide specific areas ?

In that case yes a quadtree can be used to control subdivision, but try to be more specific with your question. What do you intend to do and at which specific point are you stuck ?

Overdrivr
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