This image really consists of one image processed individually and multiply in various editing apps, then added to Diptic to a 4 x 4 grid. Here are the simple steps:
1) Do all basic editing needed to the original image (contrast, cropping, etc.)
2) Process the resulting image as desired.
3) In Diptic, select the 4 x 4 grid and add the image (or the image you desire) into each box. Make sure all images align similarly in each frame (so that they match).
4) Adjust the border to your preferences (color and thickness)
5) Make sure you export the resulting 4 x 4 grid image in high resolution.
6) Open Diptic again (or select Layout and select the 4 x 4 grid again -- if you did not quit the app it should already be the one you are using)
7) Add the original 4 x 4 grid generated into one of the frames (boxes) in the new 4 x 4 grid you are creating. Repeat that procedure for each of the frames in the grid. The result will be a 4 x 4 grid that contains another smaller 4 x 4 grid in each of the frames -- for a total of 16 images.
8) Remember to play with the effects and transform features to your liking (border size, color, as well as mirroring the image in the frame).
From there you can take the image anywhere you'd like. Each sphere in the above image was also processed in different apps (Pic Grunger, Photo FX, Iris Photo Suite, etc.). I also added some visual perception differences to the grid. The final image could also be processed according to your preferences and artistic vision. My next project is a composite grid of self-portraits. What's yours?