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This is a design principle based on a cornucopia shape - so that
materials can be designed so that, rather than either having a
consistent density or an articulated structure (being composed of a
hard "bone" structure, flexible "skin" structure and a connective
"muscle" structure), materials
can instead be designed based on a
density-faded principle where rigidity is mapped into a cornucopaic
"filling" of the area of an object and flexibility surrounds the rigidity
incrementally through the use of graduated spacing of pixles as
printed on a 3d printer. So instead of bones and skin you would
have bones fading into skin with no hinge. Graduated density
fading. And so I imagine that the most flexible and strong shape
that you could map into an object would be a single coil möbius
spring - the closest approximation to infinitely mixable fluid
dynamic motion. So spring things.
Patio chair with cornucopia design (but not density fading)
[JesusHChrist, Oct 09 2011]
||There are entirely too many theoretical physicists out here
in the snow...
||//And so I imagine that the most flexible and strong shape that you could map into an object//
||Is there some elision of the thought here? I mean, taken literally, this seems redundant, in the sense that a shape that you *couldn't* map into an object couldn't really be thought of as flexible or strong, could it? Or does "map" somehow mean "build with a 3-D printer"? That would be OK, but you should specify it, if that's what you mean.
||There are some materials, like increasingly-cross-linked plastics, where this might produce interesting properties, but there are a great many where the changes in material grain structure would force hard transitions between states.
||This reads like a semi-gelled pudding of thought-in-process, I suggest you rewrite and clarify a bit when you reach the more solid end.