Editing A New Kind of Science (section)

===Simple programs===
The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary [[computer program]]s. In almost any class of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops, applying the same simple set of rules on itself, similar to a self-reinforcing cycle using a set of rules). This seems to be true regardless of the components of the system and the details of its setup. Systems explored in the book include, among others, cellular automata in one, two, and three dimensions; [[Mobile automaton|mobile automata]]; [[Turing machine]]s in 1 and 2 dimensions; several varieties of substitution and network systems; recursive functions; nested [[recursion (computer science)|recursive functions]]; [[combinator]]s; [[tag system]]s; [[register machine]]s; and [[Palindromic number|reversal-addition]]. For a program to qualify as simple, there are several requirements:
# Its operation can be completely explained by a simple graphical illustration.
# It can be completely explained in a few sentences of [[human language]].
# It can be implemented in a [[computer language]] using just a few lines of code.
# The number of its possible variations is small enough so that all of them can be computed.

Generally, simple programs tend to have a very simple abstract framework. Simple cellular automata, Turing machines, and combinators are examples of such frameworks, while more complex cellular automata do not necessarily qualify as simple programs. It is also possible to invent new frameworks, particularly to capture the operation of natural systems. The remarkable feature of simple programs is that a significant proportion of them can produce great complexity. Simply enumerating all possible variations of almost any class of programs quickly leads one to examples that do unexpected and interesting things. This leads to the question: if the program is so simple, where does the complexity come from? In a sense, there is not enough room in the program's definition to directly encode all the things the program can do. Therefore, simple programs can be seen as a minimal example of [[emergence]]. A logical deduction from this phenomenon is that if the details of the program's rules have little direct relationship to its behavior, then it is very difficult to directly engineer a simple program to perform a specific behavior. An alternative approach is to try to engineer a simple overall computational framework, and then do a [[brute-force search]] through all of the possible components for the best match.

Simple programs are capable of a remarkable range of behavior. Some have been proven to be [[universal computer]]s. Others exhibit properties familiar from traditional science, such as [[thermodynamics|thermodynamic]] behavior, [[continuum mechanics|continuum]] behavior, conserved quantities, [[percolation]], [[sensitive dependence on initial conditions]], and others. They have been used as models of [[traffic]], material fracture, [[crystal growth]], biological growth, and various [[sociology|sociological]], [[geology|geological]], and [[ecology|ecological]] phenomena. Another feature of simple programs is that, according to the book, making them more complicated seems to have little effect on their overall [[complexity]]. ''A New Kind of Science'' argues that this is evidence that simple programs are enough to capture the essence of almost any [[complex system]].