To illustrate the method, we choose , and
so that so that
the data will always appear uniformly distributed
when projected on a plane.
Figure 5.8 shows the data as seen from
the plane after 4 and 20 iterations
of the systematic method.
The five facets of the valid region are caused by the manifold
reaching the positivity limit of each of the five dimensions.
Non-uniformity can be clearly seen for 4, but not for 20
Later, we will discuss the difference between the
systematic and the random-directions algorithm.
But first, we must solve for the asymptotic mean.
Visual uniformity test for , . The 2-D manifold as seen from the
two dimensions after 4 iteration (left)
and 20 iterations (right).