I myself am creating a terrain generation algorithm and would be interested in knowing why others have chosen midpoint displacement over perlin noise. Minecraft is an example where midpoint displacement was preferred. If anyone knows why I would be glad to hear it.
Answer
Different methods of fractal generation tend to produce terrain with different characteristics. The reason for their use could be stylistic rather than for any technical performance reason. Different algorithms also allow you to change different parameters to give the final result. I have no direct answer re: MD vs Perlin though, sorry..
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