Inspired by isomage's efforts at random cave generation I did a bit of research on random walks and came across this description on simulating bacteria using random walks with a gradient bias.

I turned to my trusty swiss army knife, processing and cobbled together a random walk with gradient bias engine....then started building gradients to make gave maps.

My first experiment was just to verify the algorithm would follow random walk along the gradient from light to dark.

The gradient:
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and the walk:
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Then I came up with this perlin noise with a left to right bias map:
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which created this "cave" structure
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and here is a comparison showing the lineup:
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I think there could be some promise in this...

-Rob A>