A few things more...

• Surely "phase difference" does not necessarily have to be half the width of the "slice frame". For example, with a slice frame that is to be 30 pixels wide, the phase difference doesn't have to be 15 pixels, and it can surely be 10 pixels, etc., depending on the effect that one wants to achieve. The only important thing seems to be that it makes things (framing slices with equal dimensions throughout the image) easier to chose numbers as common multiples and/or common divisors for each other: an image 800 pixels wide, a slice frame 40 pixels wide, a phase difference of 20 pixels (or 10 perhaps), as an example...
• The lesser the phase difference, the longer (thus larger) the resultant image. For example, while keeping the phase difference as "1/2" the width of the slice frame is like merging "2" images into each other in slices, keeping the phase difference as "1/3" the width of the slice frame is like merging "3" images, and so on...