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In-Depth Information
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FIGURE 10.24
The
D
2
lattice.
FIGURE 10.25
TheA
2
lattice.
granular noise. When comparing the square and circle as candidates for quantization regions,
we used the integral over the shape of
2
. This is simply the second moment of the shape.
The shape with the smallest second moment for a given volume is known to be the circle in
two dimensions and the sphere and hypersphere in higher dimensions [
150
]. Unfortunately,
circles and spheres cannot tile space; either there will be overlap or there will be holes. As the
ideal case is unattainable, we can try to approximate it. We can look for ways of arranging
x
