What is the picture of Gamma regularization in convex conjugate?

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In the theory of convex conjugation, it is said $F\ge F^{**}$. Here $F^{**}$ is said in fact the Gamma regularization of $F$.

My question is that: is there any nice picture to understand the Gamma regularization? And when will $F\neq F^{**}$ (i.e. $F> F^{**}$)? is there any simple example?

As a picture, I know $F^{**}$ is kind of points from the set of tangent superplanes (Correct me if I am wrong). But I dont know when the set of tangent superplanes can not represent the original one, i.e. when $F\neq F^{**}$?