A Voronoi diagram is a way of decomposition or subdivision of space based on an initial set of objects or points (for more information http://en.wikipedia.org/wiki/Voronoi). Voronoi diagrams have countless applications from statistics to biology and urban planning. Lately they are becoming ‘popular’ also in architectural design. There are indeed a number of reasons making Voronoi diagrams useful in architectural design:[source http://object-e.blogspot.com]
a. Their structural properties, both in 2d and 3d.
b. As a way to subdivide/organize space, based on proximity/closest neighbor.
c. The fact that they can describe many natural formations, like soap bubbles, sponges or bone cells.
And we need to be a bit critical about this :So yes, let's not make a Voronoi cool looking structure because it looks cool, it is not taking anyone anywhere...
"the real question is why would you want to make a Voronoi (or any algorithm) to begin with? What is it responding to within the discourse?
Rather, what do any of these parametric exercises offer an architect beside something that 'looks cool' or 'looks complex' or 'looks irregular'? It's not like you can plug programmatic or site or material data into it, it is all geomtric "input." This way of working seems more like pure geometry and little bit of structure. It's not like you are done once you have your honeycomb mesh." [source : http://www.archinect.com]
Because we are armies of cool people doing this research already :
And one of the best sources is here (about the algorythmic beauty of plants) :
like this one:
And again, this is how some people use their Voronoi background to semi-aumotate the building of a "rational city" [source http://twak.blogspot.com]: