Black and white floor tiles for the bathroom have a long history. They were popular during the Victorian times and during the Arts and Crafts period. The style has been copied in vinyl form, but there are many elegant versions available today. White hexagon tiles can be used with contrast dots, or with contrast circles which look like flowers. Or you can go with simple square tiles in various sizes and patterns. And then there is the pinwheel design, with its lovely geometric symmetry.
My favorite is the basketweave, which looks lovely in tile but also in its marble version, which stains more easily (but in the unlikely event that marble chips or scratches, no ugly under layer is revealed because stone is solid through and through, unlike tile).
What is so great about black and white floor tile is that it melds beautifully with very modern bathrooms as well as more traditional rooms. You can play up the black and white theme throughout the room or let the floor function as a neutral palette.
Basketweave tile from House and Home
Basic black and white pinwheel tiles. Alex's Granny Chic.
Marble basketweave from DIY Del Ray
Black and white checked at Brabourne Farm
An interesting combination of large marble squares and a criss cross design of black tiles from Brabourne Farm
Close-up of marble basketweave from Vector East
Stunning bathroom with simple hex pattern designed by Webber + Studio via Houzz
Donna DuFresne Design hex tile pattern via Houzz
9 The Little House in the City
: an example of hex black and white tile (slightly bigger than usual)
(Images: as linked above)