How to display post from current Taxonomy in archive page?

I am using the following code to display a random post from the current category in category archive page (using archive.php). However, when in Tag or Taxonomy archive pages, the post is not correctly displayed from the current Tag or Taxonomy (due to the limitation of category only). How can I modify to make it work with Tag and Taxonomy (or just Taxonomy since Category and Tag are also Taxonomies). Thanks!

// assign the variable as current category
$currentcategory = $cat;

// concatenate the query
$args="showposts=1&cat=" . $currentcategory . '&orderby=rand';

$random_query = new WP_Query( $args );

// The Loop

if ( $random_query->have_posts() ) {
while ( $random_query->have_posts() ) {
$random_query->the_post();

// custom template for the random post

}

} else {

// no posts found

}

// Restore original Post Data
wp_reset_postdata();

Edited code in regarding to s_ha_dum’s answer:

<?php // The Query

if (is_tax() || is_category() || is_tag() ){
    $qobj = $wp_query->get_queried_object();

// concatenate the query
    $args = array(
        'posts_per_page' => 1,
        'orderby' => 'rand',
        'tax_query' => array(
            array(
                'taxonomy' => $qobj->taxonomy,
                'field' => 'id',
                'terms' => $qobj->term_id
                )
            )
        );
}

$random_query = new WP_Query( $args );

// The Loop
if ( $random_query->have_posts() ) {
    while ( $random_query->have_posts() ) {
        $random_query->the_post(); ?>

//HTML tempalte

<?php   }
} else {
    // no posts found
}
/* Restore original Post Data */
wp_reset_postdata(); ?>

You will need to grab the queried object for the page and fill in your taxonomy information dynamically.

if (is_tax() || is_category() || is_tag() ){
    $qobj = get_queried_object();
    // var_dump($qobj); // debugging only
    
    // concatenate the query
    $args = array(
      'posts_per_page' => 1,
      'orderby' => 'rand',
      'tax_query' => array(
        array(
          'taxonomy' => $qobj->taxonomy,
          'field' => 'id',
          'terms' => $qobj->term_id,
    //    using a slug is also possible
    //    'field' => 'slug', 
    //    'terms' => $qobj->name
        )
      )
    );

    $random_query = new WP_Query( $args );
    // var_dump($random_query); // debugging only

    if ($random_query->have_posts()) {
        while ($random_query->have_posts()) {
          $random_query->the_post();
          // Display
        }
    }
} 

It is not clear if you need this Loop in addition to the main Loop or as a replacement for it. I am assume this is “in addition” as it would effectively remove archive functionality if it were to replace the main query. You;d have no real archives, just a random post from the archive which isn’t very friendly all by itself.

You could use the category.php and the tag.php archive templates to process tags and categories separately. You don’t need to use archive.php.

Reference

http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters
http://codex.wordpress.org/Function_Reference/get_queried_object