Almost all the science that's been done for the past three hundred or so years has been based in the end on the idea that things in our universe somehow follow rules that can be represented by traditional mathematical equations. The basic idea that underlies research in NKS is that that's much too restrictive, and that in fact one should consider the vastly more general kinds of rules that can be embodied, for example, in computer programs.
Instead of asking what mathematical equation some system obeys, it asks what simple program produces the behavior seen in that system. Pure NKS investigates how various types of simple programs typically behave - much as traditional mathematics examines various mathematical equations. Applied NKS then looks for simple programs behind the behavior seen in natural and other systems.
As Kepler noticed orbits seem to follow ellipses, Wolfram noticed things like a seashell pattern that seems to follow a 1-D cellular automaton, and a 2-D hexagonal grid cellular automaton that seems to reproduce the basic forms of snowflakes. Instead of conic sections or differential equations, NKS considers Turing machines, cellular automata, or other similar programs following simple definite rules.
The world of simple programs is another, very general set of formal patterns that real systems can be based on, beyond the equation based patterns investigated in the past. Despite the simplicity of the underlying rules, these programs can exhibit behavior of immense complexity. This conference brings together researchers whose work is established on the principle that this is the basic mechanism nature uses to produce the wealth of complexity we see all around us.