Category Child Of not functioning

i would expect a kind of foreach loop to show all child categories.

you only seem to work with one term: $term = $categories[$i];
where is the $i defined?
was that planned to be a for loop?
https://php.net/manual/en/control-structures.for.php

from your (incomplete) code segment, it is difficult to see what you are trying to achieve.

Sorry, I have basically got it too loop the child categories of a set parent. However I have 2 columns so need them to go in order say:
Category 1 – Col 1, Category 2 – Col 2, Category 3 – Col 1 etc etc

I have got this to work, however it doesnt seem to pick the category up correctly

My full code is:

<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>

<?php
$cats=array(
'child_of'                 => 4
	);
$categories = get_categories($cats);

?>
<div id="articles-left">
<?php
  if ($categories) {
    $numcategories = count($categories);
    for($i = 1; $i < $numcategories; $i = $i + 2) {
	$term = $categories[$i];
	echo '
		<div class="articles-post">
		  <div class="articles-posttitlebox"><a href="' . get_category_link( $term->term_id ) . '">' . $term->cat_name.'</a></div>
<img src="/wp/wp-content/uploads/category-images-ii/'.$term->term_id.'.original.jpg">
		</div>';
	}
  }
?>

</div>

<div id="articles-right">
<?php
  if ($categories) {
    $numcategories = count($categories);
    for($i = 2; $i < $numcategories; $i = $i + 2) {
	$term = $categories[$i];
	echo '
		<div class="articles-post">
		  <div class="articles-posttitlebox"><a href="' . get_category_link( $term->term_id ) . '">' . $term->cat_name.'</a></div>
<img src="/wp/wp-content/uploads/category-images-ii/'.$term->term_id.'.original.jpg">
		</div>';
		}
  }
?>

</div>
<?php endwhile; else: ?>
<p><?php _e('Sorry, no posts matched your criteria.'); ?></p>
<?php endif; ?>