The binary bumblebee "puzzle" is a version of Steven H. Cullinane's
Diamond 16 puzzle but controlled not with JavaScript but instead by
an IRC bot living on the private tilde.town server. The puzzle works
by allowing you to swap any two rows, columns, or quadrants of a 4×4
grid; these transformations interact to produce a very large number of
different highly symmetric grids.  In order to actually manipulate the
puzzle, simply join #bots on the private IRC (if you do not have a tilde.town
account, I highly recommend you get one!) and issue the command
                        !bswap ##
where each # represents one of the following characters:
     ROWS                 COLUMNS                 BOXES
     1───                  abcd                   w┐x┐
     2───                  ││││                   └┘└┘
     3───                  ││││                   y┐z┐
     4───                  ││││                   └┘└┘

You can either attempt to make one of the configurations in Cullinane's
page, or simply play around with the bwap command and have fun
without a particular goal, just admiring the pretty pictures.