The above app is used to blow up and enlarge photos, not compress them! I agree with you though, a green dot in a photo is a green dot. It bears no relationship with the light green dot next to it.
I presume however that “Genuine Fractals” lets you define objects in the photos, either manually or semi/automatically. That’ll work well for photos with large blocks of single/similar colours such as portraits, but detailed photos would probably suffer.
The application docs talk about outputting file sizes in excess of 64MB. A file of that size should be enough to store a mathematical description of most photos. I may download the demo and take a look at it.