Block/mosaic type homepage with heavily interactive menu
There is a module to do that, but you have to customize it. It have the animation option using filter, probably you can try to use that filter as menu or change that filter like menu using CSS.

Views Quicksand see the Demo and website using Drupal.


  Quicksand is a JQuery Plugin that provides a nice animation for
  filtering or reordering lists of content. Views Quicksand integrates this effect into Views. Therefore it provides a views style-plugin, which allows you to alter most settings the quicksand plugin provides.