Figure 12

Notice that the contours, instead of being diamonds and rectangles,
have become much more circular.
The reason for this is briefly as follows:
convolution of a rectangle with itself many times
approachs the limit of a **Gaussian** function.
(This is a well-known result called the
``**central-limit theorem**.''
It is explained in section .)
It happens that the convolution of a triangle with itself
is already a good approximation to the Gaussian function
*z*(*x*)= *e*^{-x2}.
The convolution in *y* gives *z*(*x*,*y*)=*e*^{-x2-y2}= *e*^{-r2},
where *r* is the radius of the circle.
When the triangle on the 1-axis differs in width
from the triangle on the 2-axis,
then the circles become ellipses.

10/21/1998