FIGURE 36. Fish and Scales, by M. C. Escher (woodcut, 1959).luted "copy" of the entire fish-and so there is more than a grain of truth to
the Escher picture.
What is there that is the "same" about all butterflies? The mapping
from one butterfly to another does not map cell onto cell; rather, it maps
functional part onto functional part, and this may be partially on a macro-
scopic scale, partially on a microscopic scale. The exact proportions of parts
are not preserved; just the functional relationships between parts. That is
the type of isomorphism which links all butterflies in Escher's wood engrav-
ing Butterflies (Fig. 37) to each other. The same goes for the more abstract
butterflies of Gplot, which are all linked to each other by mathematical
mappings that carry functional part onto functional part, but totally ignore
exact line proportions, angles, and so on.
Taking this exploration of sameness to a yet higher plane of abstrac-
tion, we might well ask, "What is there that is the 'same' about all Escher
drawings?" It would be quite ludicrous to attempt to map them piece by
piece onto each other. The amazing thing is that even a tiny section of an
Recursive Structures and Processes 147