Maybe some variation of a hopscotch pattern?

Here is a link that might be useful: Daltile Multiple Tile Patterns

It looks like an Ashlar pattern, or a modified one.
Only concerns I would have with slate in a kitchen is oil/grease darkening near the cook and prep areas, and the cold/hardness underfoot. If you are ok with a "living" finish, it would be very appropriate in a mid century, and a cool look.

Thank you both! Those would both be good 'nuff for me! I should have known Daltile would have something in their tile planner!

Yeah slate is a tricky one...I don't know if it could be sealed adequately but perhaps another dark grey stone would work. Living finish is one thing. Gross is another!

I like squishy floors but I don't know if I can put linoleum in a family room and they're going to be very open to one another (pretty much in the same room). And then there's the kids and dog and they (okay, mostly me but a little bit them) have messed up the oak in the existing house so some sort of hard, unforgiving surface makes sense.

We had such a floor in our entry hall in a colonial which was built about 1959-62 in southwest Connecticut.

It was significantly less bumpy than fori's example.

The midcentury variation was often more like this

Here is a link that might be useful: Vermont Slate

Also I think the pattern with this many sizes is called Versailles, or French pattern. Google it, it looks like it to me.

I thought Versailles had a repeating pattern and I don't see that here ... ?

Fori, have you considered a slate-look porcelain? You might find one in sizes available to create a Versailles pattern.

The couple at YHL just cleaned up their slate floor. Love the look.

Here is a link that might be useful: YHL Slate Floor

That slate floor is absolutely gorgeous. My brother has Brazilian grey slate in his 1950s renovated kitchen. He sealed it and has not had a single issue. His tile is a little more smooth than that. I have ostrich gray slate in my foyer, laundry room, and powder room. And I intend to install the same slate in my kitchen (have a stack of it waiting in the basement). I think slate tile floors are fantastic for kitchens and would work really well in a family room with rugs for a little softness underfoot.

Slate is wonderful but yearly sealing would be a good idea in a kitchen. It's very porous and the sealant wears off.

Thanks so much all!

I think I've got the spouse on board. The breakfast area will open out onto a covered patio and I could spill the slate out there maybe. (I assume it would be too hot to use in uncovered parts of the yard, but maybe I should visit the Pool Forum....)

I've considered porcelain but nahhhh it's just not the same somehow! :) If I were doing porcelain/ceramic, I'd go all out with saltillo which I could probably pull off being in CA. Or terrazzo which would probably be too awesome for me to pull off! (We're adding a small bath though and I may go full-on glitter in there.)

I was thinking of starting with filthy colored grout so I wouldn't notice staining--Pricklypear, what type of grout do you have and does it stain? Maybe I don't need to start with dirt colored grout...

Love the floor on YHL! And I do have a spot or two where I could test out that product.

fori, I have a slate patio and slate walkways all around my house (So Cal) and it is not hot at all. Staining has not been a problem with our natural grey grout, even being outdoors, though we do periodically reseal the stone/grout.

We have duraceramic in our bathrooms. It's a composite tile with a vinyl overlay. It can be grouted. It is so easy to clean and has worn sooooo well. They have tiles that look like slate. They can even be cut to different sizes.

Here is a link that might be useful: Duraceramic

"stat with filthy-colored grout." Maybe that should be a color name! I would never be good at marketing...

we had similar black slate in our MCM. I was told by my tile installer it was called a Mondrian pattern. It had clearly not been sealed in many years and was in such bad shape we decided not to salvage it and replaced it with a lighter tile.