This creates a matrix of 0s containing a radius 4 diamond of 1s. The result is a 9×9 matrix:

The size of the matrix can be explicitly specified:

This creates a matrix containing an ellipse and displays it graphically:

Here is the same matrix, converted to an Image. Note that 1 is White and 0 is Black:

The shape matrix family of functions can make arrays with any rank:

This creates a radius 2 Gaussian kernel:

GaussianMatrix can construct arrays with any rank:

By default, the matrix elements are numerical and constructed to behave optimally under discrete convolution. Using WorkingPrecision->Infinity will produce an exact representation:

Use Method->"Gaussian" to sample a true Gaussian:

This shows a comparison of the two types of Gaussians:

This specifies a standard deviation of 1 in both directions of a rectangular Gaussian matrix:

Plot the second derivative of the Gaussian in the row direction:

Sum derivatives by using nested List objects in the second argument. For example, this plots the Laplacian:

This finds the length of the vector which has a minimum of 95% of the integrated fraction of the Gaussian with standard deviation 1:

This finds the dimensions of the matrix which, in each direction, has a minimum of 95% of the integrated fraction of the Gaussian with standard deviation 1: