From your answer, it may be dependent on the version of the Apple TV. Mine is the first "generation" Apple TV, the one with it's own built in hard disk. The pictures are moved from the Mac to the hard disk on the Apple TV by wifi before they can be viewed. The pictures are placed in a folder(on the Mac) that is "shared" with the Apple TV. After the move, the computer need not be turned on. The newer Apple TV's (without the hard disk) must work differently, perhaps moving the pictures, in real time, from the computer as they are viewed on the Apple TV . I can't remember seeing any option for shuffle viewing. The sequence on the Apple TV are not fully randomized (my error previously) but merely somewhat out of order.

I want to send a set of photos from my Mac to my Apple TV. The problem is that the sequence of the photos is randomized on the Apple TV , i.e. different from the sequence in a folder on the computer. Same thing happens if I view a folder of pictures using "preview". They end being out of order, just like on the Apple TV. The sequence is not a function of the file name.
One theory is that the photo sequence (Apple TV) is based on the modification date of the photo, not the creation date, a bug in iTunes. Anyone else bothered by this or if so, is there a solution ( to maintain the correct sequence)?