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InfluxDB
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To generate the point distributions you need, you could probably use this ChunkPointGatherer class I wrote for another project, and its dependency UnfilteredPointGatherer. Port to whatever language you need, of course. Here is my understand of how to implement this:
The resulting paths will all be straight, unless you do something to improve this. One idea, is to use domain warping noise. Another idea would be to pick a direction at each point based on its neighbors values, and try to curve the connecting segments towards those directions.