Space Divison

The function which is calculated inside the considered volume is F = cos(x) + cos(y) + cos(z). The set of points at F = 0 forms the depicted surface.

Space Division
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This surface divides the space into the negative and the positive part of the function. The function is symmetric in the sense that it has the same amount of positive and negative values and even more, just by shifting the function by pi into any direction, it maps the positive part onto the negative one. It is periodic in 2*pi and it has mirror symmetry around n*pi, with n any integer number including negative ones and zero. Thus it follows that the outer side of the surface (the green one) can be conformal mapped onto the inner side (the orange one). This is clearly visible in the truncated surface quarter.

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