Directional sampling [in cellular automata] One can consider sampling cells not in a vertical column but on lines at any angle.

In dolphins, it is known that one dolphin can produce patterns of sound that are repeated by a specific other dolphin.

Ingredients for complexity With its emphasis on breaking systems down to find their underlying elements traditional science tends to make one think that any important overall property of a system must be a consequence of some specific feature of its underlying construction.

Note that much as on page 662 one can construct universal circuits that can be arranged by appropriate choice of parts of their input to compute any function of a given input size.

3n+1 problem as cellular automaton If one writes the digits of n in base 6, then the rule for updating the digit sequence is a cellular automaton with 7 possible colors (color 6 works as an end marker that appears to the left and right of the actual digit sequence): {a_, b_, c_}  If[b  6, If[EvenQ[a], 6, 4], 3 Mod[a, 2] + Quotient[b, 2] /. 0  6 /; a  6] The 3n+1 problem can then be viewed as a question about the existence of persistent structure in this cellular automaton.

Multiplicative digit sequences One can consider generalizations of digit sequences in which numbers are broken into parts combined not by addition but by multiplication.

Finding primes The sieve of Eratosthenes shown in the picture is an appropriate procedure if one wants to find every prime, but testing whether an individual number is prime can be done much more efficiently, as in PrimeQ[n] in Mathematica, for example by using Fermat's so-called little theorem that Mod[a p - 1 , p]  1 whenever p is prime.

[Classes in] continuous cellular automata In ordinary cellular automata, going from one rule to the next in a sequence involves some discrete change.

One can also consider higher-order Voronoi diagrams in which each region shows where a given point is the k th closest.

Origins of localized structures Much as with other features of behavior, one can identify several mechanisms that can lead to localized structures.