Creative Ecosystems - Computers and Creativity - page 41

comprise the image. Iterating through each co-ordinate, the expression returns the
corresponding pixel's colour. Different expressions will usually generate different
images (although many different expressions will also generate the same image). In
theory, this system is capable of generating any possible image, provided you have
the appropriate Lisp expression to generate it.
This represents a space of possibilities than encompasses every possible image
that can be represented by coloured pixels over (x, y) . For any reasonable image
dimensions, the size of this space is Vast, far beyond comparisons with astronom-
ical maximums such as the age of the universe, or the number of basic sub-atomic
particles estimated to exist in the universe.
However, the actual space of images that can be practically created with a Lisp
expression is considerably smaller, limited by physical constraints. From the per-
spective of evolutionary creativity, if we evolve a Lisp expressions using, for ex-
ample, an Interactive Genetic Algorithm (IGA, see Sect. 2.2 ), the actual images
produced are all relatively similar and represent an infinitesimally small fraction
relative to the possible space of which the system is theoretically capable. 1
So while a representational system may theoretically cover a large range of possi-
bilities, searching them—even with evolutionary methods—will only permit exami-
nation of insignificantly small regions. Furthermore, transformation or modification
of the underlying generative mechanism 2 may open up new spaces not so easily
found by the original, e.g. the addition of symmetry functions for the Lisp expres-
sion example would make it easier to generate images with symmetric elements. Of
course we need some way of finding the “right” transformations or modifications to
make. This is a kind of “meta-search” (a search of the different types of generative
mechanisms that define a representational space). Further, this opens a hierarchy
(meta-meta-search, meta-meta-meta-search, etc.), which effectively amounts to the
same problem of the possible and actual in our original “flat” search.
What this means in practical terms is that there must be some human-defined
generative mechanism as the basis for any computational creative system, 3 which
will require serious human ingenuity and creativity if it's design is to be effective.
I will return to this point in Sect. 2.4.3 . While much research effort and discussion
has focused on evaluation and judgement in computational creative systems, repre-
sentation has received far less attention.
A somewhat analogous situation exists in biology. The space of possible DNA
sequences is far greater than the space of viable, or possible, phenotypes. 4 The space
of possible phenotypes (those which could exist) is again larger than the space of

1 By my estimates, about 5

10 − 1444925 × % for images of modest dimensions, far beyond astro-

nomically small.
2 By “generative mechanism” I am technically referring to the genotype and the mechanism that
expresses it into a phenotype.
3 The mechanism can include the ability to self-modify, change, or learn.
4 We might think of “viable” as meaning being able to effectively express a living organism from a
zygote or through mitosis of a parent cell. But this is problematic for many reasons, most of which
are too tangential to the argument to list here.