Wolfram Research, and Stephen Wolfram, were honored
by the invitation to be a part of the "Leonardo
da Vinci: Man, Inventor, Genius" exposition at Chicago's Museum of
Science and Industry. Here is information about some of the objects that
were on display.
A New Kind of Science
Objects like those pictured below are discussed
in Chapter 5 of Stephen Wolfram's
book A New Kind of Science (NKS). These
three-dimensional cellular automata
all use growth rules—a cell gained is gained
forever. For all of these, the simple rule is a cell is gained
where it would touch exactly two others. Simple rules can lead
to very complex systems.
All of the objects here were initially visualized
with Mathematica, applying NKS methods. Here is a
Mathematica notebook you can download that
has code for the objects displayed on this page; if you don't have Mathematica, you can get a trial version. Below, you can see
the objects as they initially appeared in Mathematica.