1D-symmetry of A Function Vs. 2D-symmetry of Its Graph
Symmetries of a function (in the sense of this article) imply corresponding symmetries of its graph. However, 2-fold rotational symmetry of the graph does not imply any symmetry (in the sense of this article) of the function: function values (in a pattern representing colors, grey shades, etc.) are nominal data, i.e. grey is not between black and white, the three colors are simply all different.
Even with nominal colors there can be a special kind of symmetry, as in:
−−−−−−− -- − −−− − − −(reflection gives the negative image). This is also not included in the classification.
Read more about this topic: One-dimensional Symmetry Group
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