The initial condition consists of a block of length 41 inserted between blocks of the background.

And even though there is no explicit randomness inserted into the model in any way, the paths of the cracks that emerge nevertheless appear to be quite random. … Even though no randomness is inserted from outside, the paths of the cracks that emerge from this model nevertheless appear to a large extent random.

Simulating mobile automata Given a mobile automaton like the one from page 73 with rules in the form used on page 887 —and behavior of any complexity—the following will yield a causal-invariant substitution system that emulates it: Map[StringJoin, Map[{"AAABB", "ABABB", "ABAABB"} 〚 # + 1 〛 &, Map[Insert[# 〚 1 〛 , 2, 2]  Insert[# 〚 2, 1 〛 , 2, 2 + # 〚 2, 2 〛 ] &, rule], {2}], {2}]

The basic way this can be done is by breaking a connection coming from a particular node by inserting a new node and then connecting that new node to nodes obtained by following connections from the original node. … In both cases, a new node is inserted in the "above" connection from each existing node in The evolution of network systems with four different choices of underlying rules.

Another initial condition [for rule 90] Inserting a single in a background of blocks in rule 90 yields the pattern below in which both the white and striped regions have fractal dimension 2.

Note that the first replacement only removes elements and does not insert new ones.

Particles are inserted in a regular way at the left-hand end so as to maintain an overall flow speed equal to about 0.4 of the maximum possible.

In other systems, there is no such direct way to insert such results into the rules for the system.

So what this means is that the randomness we observe in fluid flow cannot simply be a reflection of randomness that is inserted through the details of initial conditions. … And so, once again, just as for many other systems that we have studied in this book, there is little choice but to conclude that in a turbulent fluid most of the randomness we see is not in any way inserted from outside but is instead intrinsically generated inside the system itself.

A steady stream of particles is inserted in a regular way far to the left, with an average speed 3/10 of the maximum possible.