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Studying nonlinear dimension reduction topics I came across a "horseshoe distribution" or "horsheshoe phenomena". Figure (b) [source, p. 12] depicting horseshoe distribution is included below.

Horseshoe distribution.

I do not have a good idea how to simulate this type of distribution.

Thanks in advance for any pointers.

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You could simply formulate a parabolic function fo each fixed value in a particular dimension (say for the z axis) and add a random noise component to it.

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