Output random (custom) image size

I don’t think there exists such function in the WordPress core.

Example #1

But you can try something like this:

/**
 * Random image size
 * @return String Image size
 */
function wpse_random_image_size()
{
    $sizes = (array) get_intermediate_image_sizes();
    return $sizes[array_rand( $sizes )];    
}

to display a random image size.

Usage:

if ( function_exists( 'wpse_random_image_size' ) )
    echo wpse_random_image_size();

Example #2

If you want to exclude certain image sizes, e.g. thumbnail and medium then you can use:

/**
 * Random image size     
 * @param  Array | String  Sizes to exclude
 * @return String          Image size
 */
function wpse_random_image_size( $exclude="" )
{
    $sizes = array_diff( (array) get_intermediate_image_sizes(), (array) $exclude );
    return $sizes[array_rand( $sizes )];    
}

Usage:

if ( function_exists( 'wpse_random_image_size' ) )
    echo wpse_random_image_size( $exclude = ['thumbnail', 'medium' ] );