Spontaneous symmetry breaking is one of the beautiful phenomenas of theoritical physics. It involves the creation of a true vacuum from a false vacuum. In early universe the higgs boson is supposed to get trapped in the true vacuum and acquire a vacuum expectation value (vev). Some other particles may sort of cause the higgs boson to rise uphill and increase the potential. This is analogous to say mass is acquired by that interacting particle. The similar phenomena occours in superconductivity as well. Read more about spontaneous symmetry breaking on wikipedia.
I've used the potential of the type -x^2 + x^4 which is the standard mexican hat potential or the higgs potential. Both 2D and 3D version are done.
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2D version
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3D version
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