Magic Eye: A New Way of Looking at the World
These images are called stereograms, or images that convey a sense of depth to the viewer through several different methods.
The best method, in my opinion, is to:
1.) Enlarge the image
2.) Hold it close to your nose, and look through the image.
3.) Slowly pull the image away, focusing past the image.
4.) Continue to look past the image as it becomes more detailed.
Mentalfloss explains here how, for some, this is an impossible feat. Vision therapists even use these images for treatment of binocular vision disorders.
They are beautiful, complicated images, even without the hidden message. The intersection between art and science creates a beautiful result.