Shortcode with pagination advancing multiple queries

I did a gallery pagination by converting all the stuff from galleries into arrays, and then json_encoding that and passing it to javascript.
If you were to to that you could have multiple scripts:

jQuery(document).ready(function( $ ) {
var thisgallery = <?php echo the gallery; ?>
function process pagination (){
     code for pagination
}
}

And because they are all in separate jquery document ready functions they wouldn’t see each other, so they would iterate independently and without page reloads.

Edit:
The modified shortcode function would look like this:

<?php 
function picture_gallery($atts){
    extract(shortcode_atts(array(
        'rml_folder' => 1
    ), $atts));

    query_posts("post_status=inherit&post_type=attachment&rml_folder=".$rml_folder."&orderby=title&order=asc&posts_per_page=-1");
    $return_string = "";
    $pics = array();
    if ( have_posts() ) :
            while ( have_posts() ) : the_post();
                $p = array(
                    'image' => wp_get_attachment_image(get_post_thumbnail_id($post->ID), 'medium'),
                    'url' => wp_get_attachment_url($post->ID)
                );
                $pics[] = $p;
            endwhile;
    endif;
    $pics = json_encode($pics);

    $return_string .= "<div class="js-gallery-$rml_folder"></div>
    <script>
    jQuery(document).ready(function( $ ) {
        var pics = $pics;
        console.log(pics);
        $('.js-gallery-$rml_folder').html(pics[0][image]);
    }
    </script>"

    wp_reset_query();

    return $return_string;
}

Edit: added a div to show the first picture in gallery.