Sierpinski hiding in the Sistine Chapel


It was the second day in Rome, an intense day of walking and walking and WALKING, made all the harder by the youngest member of our family twisting his foot near the Colosseum.  And in a bout of bad timing, this was also the day we had tickets to the Vatican Museum (tickets that cost significantly less than 10 Billion Euros, I’m happy to say), so sore foot or not we forged ahead.

The museums were absolutely amazing, with cool things like actual Babylonian script (no idea what it means because it wasn’t clearly numbers, but still):

Plus, because it was a Friday night and the Museums aren’t always open then (last we heard it was a summer thing, extended through October), there weren’t many people in the main part of the museum.  It was dark, and we could look out from nearly empty rooms into nearly empty courtyards:

But the museums are long.  Really long.  I can’t find the dimensions, but according to my city map they look about 1/3 of a mile, and you basically walk around near the entrance then then down one whole side the entire 1/3ish mile length on the second floor, and then you go return on the bottom floor.  By the time we reached the end of the second floor we were already carrying our younger son, and we still had to walk back to get to the exit [and then walk to the Metro, and then the hotel.  And it was almost 10pm.]  But still, at this halfway point is the Sistine Chapel, and that is not to be missed, no matter how tired.

So we went in the Sistine Chapel, which was the one area that was completely crowded, plus it was really loud in there because the guards kept saying SHHHHHHHHH into the microphones and then a recorded voice came on overhead to tell everyone that this was a place of worship and to be quiet, and this was repeated loudly in 8 different languages.  So after about 15 seconds of admiring the ceiling we decided to call it a day and begin the trek back.  But then, right near the exit, TwoPi suddenly whispered, “It’s a Fractal!”  And so I looked at the floor:

See all those Sierpinski Triangles???? They go all the way to Stage 3!

The entire walk back we stopped at every souvenir stand (they’re all over the museum) and had this conversation:

“Do you have any picture of the floor of the Sistine Chapel?”
“You mean the ceiling?”
“No, the floor.”
“No, sorry.”

But then the next day we went to the Mouth of Truth (a giant face where you stick your hand in the mouth, and it gets bit off if you’re a liar), which is part of the church Santa Maria in Cosmedin.  The exit from the Mouth of Truth area goes through the church itself, and lo, there were MORE Sierpinski triangles on the floor!


and here

and smaller ones here:

and curved ones here

There were some other neat shapes, too, like these

and these, which looked just like a quilt

and these

The pieces were all laid out in sections, like…well, I really did think of quilts every time I looked at the floor:

There were even swirly parts that formed a giant infinity.

After taking 800 pictures we finally left, but a few hours later we were at the Basilica of San Clemente, which is a medieval Church built on top of a 4th century church built on top of a Temple of Mithras, and at the most modern level the floor has the same kind of design.  We sat and rested our tired feet admired it, but didn’t take any pictures because a Mass was about to start and we didn’t want to intrude.

So what was going on?  It turns out that this style of floor is called cosmatesque, and Our Friend Wikipedia describes it as:

a style of geometric decorative inlay stonework typical of Medieval Italy, and especially of Rome and its surroundings. It was used most extensively for the decoration of church floors, but was also used to decorate church walls, pulpits, and bishop’s thrones. The name derives from the Cosmati, the leading family workshop of marble craftsmen in Rome who created such geometrical decorations.

So it’s not terribly surprising that we saw three similar floors within 24 hours, even though we’d never seen anything like it before.  Sierpinski is hiding out all over the place.

3 Responses to “Sierpinski hiding in the Sistine Chapel”

  1. mantra meditation Says:

    But did you manage to extract any meaning out of all those geometric shapes? Any deep esoteric mathematical secrets? Why use those patterns?

  2. Staabmia Says:

    Is that last picture (of infinity) from the San Giovanni Cathedral? I just got back from a trip to Rome and happened to stumble upon this site. Glad I’m not the only one who found the beauty of the floors to be just as beautiful as the ceilings.

  3. Ξ Says:

    Staabmia — no, we didn’t make it to that one. The last picture is also of Santa Maria in Cosmedin, but I gather that there are several similar floors. I think I could have just looked at floors and ceilings all over the city and been perfectly happy!

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