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© Copyright 1993 Mario Hilgemeier

The (Nearly) Infinite Paradise of Fractal Images

      We wish to search for beautiful images by computer. Probably 
you are using a computer monitor to watch the program-generated 
images. Let's suppose the monitor has a resolution of 1000 pixels 
(picture elements) horizontally and vertically, with 256 possible 
colors for each pixel. How big is the picture space to be traveled 
by the beauty-seeking program? That's easy to compute from 
combinatorics: 256 to the 1,000,000th power, which is roughly equal 
to 10^2,408,234. This is more than the square of a gigaplex, which 
Rudy Rucker defines as the sum of all possible thoughts of a man 
[21].  Even if we settle for a low resolution black and white 
monitor with 200*200 pixels we still have to cope with a picture 
space of 2^40,000 or about 10^12,041. If 10 billion people watched 
for 80 years (without sleeping) a picture each second, this enormous 
effort could scan only 2.5*10^19 pictures.  

      Let's suppose, a "picture space of all fractal images" can be 
defined in some way. Because the number of fractal images may be 
large, the time for "just looking at all the beautiful fractal 
images" is a lot longer than many lifetimes. This is true, even if 
you had a filter program to select for you "only the beautiful ones, 
and only one of each group of similar looking ones." If you get 
bored, you could modify your filter program to exclude "the boring 
ones" (and wait a little longer) or even trim your search algorithm 
to seek out realms in image space where "things are most unsimilar 
to things already discovered." Provided you have a "dissimilarity 
measure," you may find something new. The ultimate limits, of course, 
are a) your picture-generating program, b) time and c) the number of 
pictures that a human can distinguish (as far as I know, this is an 
unknown number but probably very large, depending on the number of 
rods and cones on the retina and the number of neurons in the visual 

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© Copyright 1993, Mario Hilgemeier, email: contact
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