As discussed on pages 44 – 50 , there were by the beginning of the 1980s various kinds of abstract systems whose rules were simple but which had nevertheless shown complex behavior, particularly in computer simulations. … And starting around the mid-1980s it began to be not uncommon to hear the statement that complex behavior can arise from simple rules—though often there was great confusion about just what this was actually saying, and what, for example, should be considered complex behavior, or a simple rule. … But despite all this, no major new scientific developments were forthcoming—not least because there was a tremendous tendency to ignore the idea of simple underlying rules and of what I had discovered in cellular automata, and instead to set up computer simulations with rules far too complicated to allow them to be used in studying fundamental questions.

In discrete systems such as cellular automata there are always a discrete set of possible rules.

Thus for example, however many times one runs a rule 30 cellular automaton, starting with a single black cell, the behavior one gets will always be exactly the same.

much more reflect explicit rules of evolution than the constraint associated with the invariant state.

The details depend on the exact rules for each program, but the overall characteristics remain very much the same.

The rule for the system places a new black dot at whatever position this concentration is largest.

With different substitution rules for each type of cell, the structure will in general be nested.

Then in the early 1970s, considerable recreational computing interest developed in a specific two-dimensional cellular automaton known as the Game of Life, whose behavior is in some respects similar to the rule 110 cellular automaton discussed in this chapter .

situations—save those associated with the overall expansion of the universe—the basic rules for the network at least on average just rearrange nodes and never change their number.

For if the underlying rule for a network is going to maintain to a certain approximation the same average number of nodes as flat space, then it follows that wherever there are more nodes corresponding to energy and momentum, this must be balanced by something reducing the number of nodes.