How to tell geometrically/graphically the statistical properties of a ring distribution?

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I pulled this distribution of a 2D random variable from page 5: https://arxiv.org/pdf/1606.05908.pdf

enter image description here

I want to know:

  1. How can we infer the covariance matrix from the plot?
  2. How can we infer the independence/dependence from the plot?

Similar to how this document breaks it down nicely for 2D gaussians: http://www.cs.utah.edu/~tch/CS4640F2019/resources/A%20geometric%20interpretation%20of%20the%20covariance%20matrix.pdf