Logic of code to determine location of images

I like to know (explanation of code) how images have been placed in the following example:

The initial order of the list of items is [3,1,2]. As the order is changed, list L reflects the new order (see the graph CL).

The center for the puppy image:

([-12,0,12],0 {L[3]=[1,2,3]})

The center for each image is actually three points. The x-coordinates are the list [-12,0,12]. The y-coordinate is 0 with a list of restrictions, where the new position in the list (e.g. L[3], the third element in list L) must equal [1,2,3]. It’s only going to be true for one of these so each image will only appear at one of the three points (-12,0), (0,0), or (12,0). Breaking down the puppy centers and writing them in a different way:

center 1=(-12,0 {L[3]=1})
center 2=(0,0 {L[3]=2})
center 3=(12,0 {L[3]=3})

So for the puppy image, it’s initial position was 2 (L[3]=2), so the image will only appear at center 2. If “puppy” in the list is moved, L[3] changes, and L[3] no longer equals 2, changing the images.

If you weren’t aware you could use lists of points for one image center in order to display it multiple times, this may not make sense.

Thank you. I appreciate your guidance.