select field with multiple sub-categories - too inefficient

I have a select box that filters categories. However, there are also sub-categories, and sub-sub-categories, etc.

  <form method="GET" action="categories.php">
    <div class="form">
      <select id="filter" size="1" name="filterCat">
        <option value="allCats" <?php if ($filterCat == 'allCats') echo 'selected="selected"';?>>All Categories</option>
        <option value="0" <?php if ($filterCat == 0) echo 'selected="selected"';?>>MAIN</option>
        <option value="noItem" disabled="disabled" >-------------------------------</option>
        <?php
			$cat_result = mysql_query("SELECT `categories_id`,`categories_name` FROM `categories` WHERE `parent_id`=0 ORDER BY `categories_name`");
			while($cat_row = mysql_fetch_assoc($cat_result)){
				$categories_id = $cat_row['categories_id']
				?>
				<option value="<?php echo $categories_id; ?>" <?php if ($filterCat == $categories_id) echo 'selected="selected"';?>> <?php echo $cat_row['categories_name']; ?></option>
				<?php
					$cat_result2 = mysql_query("SELECT `categories_id`,`categories_name` FROM `categories` WHERE `parent_id`=$categories_id ORDER BY `categories_name`");
					while($cat_row2 = mysql_fetch_assoc($cat_result2)){
					$categories_id2 = $cat_row2['categories_id']
					?>
					<option value="<?php echo $categories_id2; ?>" <?php if ($filterCat == $categories_id2) echo 'selected="selected"';?>>  - <?php echo $cat_row2['categories_name']; ?></option>
					<?php
						$cat_result3 = mysql_query("SELECT `categories_id`,`categories_name` FROM `categories` WHERE `parent_id`=$categories_id2 ORDER BY `categories_name`");
						while($cat_row3 = mysql_fetch_assoc($cat_result3)){
						$categories_id3 = $cat_row3['categories_id']
					?>
						<option value="<?php echo $categories_id3; ?>" <?php if ($filterCat == $categories_id3) echo 'selected="selected"';?>>    -- <?php echo $cat_row3['categories_name']; ?></option>
						<?php
							$cat_result3 = mysql_query("SELECT `categories_id`,`categories_name` FROM `categories` WHERE `parent_id`=$categories_id3 ORDER BY `categories_name`");
							while($cat_row4 = mysql_fetch_assoc($cat_row4)){
							$categories_id4 = $cat_row4['categories_id']
						?>						
							<option value="<?php echo $categories_id4; ?>" <?php if ($filterCat == $categories_id4) echo 'selected="selected"';?>>    -- <?php echo $cat_row4['categories_name']; ?></option>
				<?php }}}} ?>
      </select>
    </div>
  </form>

So my issue is that I repeat the code for each new sub-category, and create a new loop to look up the sub-categories belonging to that one. Is there a simpler way that will cause the categories to look up if they have any sub-categories, and then run a loop from there, i.e. infinitely, so that if there were even 10 levels of categories, it would still be able to find them all?