How can I make a page with Category Names and make them show up as a tiled-grid?

Hi everyone.
My goal is to make the homepage of my wordpress site show only the categories of my posts.

This page should show the categories as a grid of tiles, similar to the windows 8 theme I guess (for visualizations sake :wink: )

but I'm having a hard time getting this "list" (i guess it shouldn't even technically be a list in the first place?!) to show up as a grid.

Secondly, I would like to somehow randomly assign each "tile" a color. And thus when a new post creates a new category, this new categroy would also receive a background color.

I have already made my custom template for the homepage, and have included this:

<?php $args = array(
'show_option_all' => '',
'orderby' => 'name',
'order' => 'ASC',
'style' => 'none',
'show_count' => 0,
'hide_empty' => 1,
'use_desc_for_title' => 1,
'child_of' => 0,
'feed' => '',
'feed_type' => '',
'feed_image' => '',
'exclude' => '',
'exclude_tree' => '',
'include' => '',
'hierarchical' => 1,
'title_li' => __( 'Categories' ),
'show_option_none' => __('No categories'),
'number' => null,
'echo' => 1,
'depth' => 0,
'current_category' => 0,
'pad_counts' => 0,
'taxonomy' => 'category',
'walker' => null
); ?>

<?php wp_list_categories( $args ); ?>

I assume that's a start?

Thanks everyone for your help and suggestions, i'm stuck on this one! (hopefully it's not a no-brainer!)