In most plants—at least after the embryonic stage—cells typically divide only in localized regions known as meristems, and each division yields one cell that can divide again, and one that cannot. Often the very tip of a stem consists of a single cell in the shape of an inverted tetrahedron, and in lower plants such as mosses this is essentially the only cell that divides.

Power cellular automata Multiplication by m in base k corresponds to a local cellular automaton operation on digit sequences when every prime that divides m also divides k . … When m itself divides k , the cellular automaton rule is {_, b_, c_}  m Mod[b, k/m] + Quotient[c, k/m] ; in other cases the rule can be obtained by composition.

But in many cases, bones are in effect divided into sections, and growth occurs between these sections. … And the skull is divided into a collection of pieces that each grow around their edges.

As an example, one can consider a generalization of the arithmetic systems discussed on page 122 —in which one has a whole number n , and at each step one finds the remainder after dividing by a constant, and based on the value of this remainder one then applies some specified arithmetic operation to n .

Note that if n is not between 1 and 4, it must be multiplied or divided by an appropriate power of 4 before starting this procedure.

What I do here is simply to divide the whole width of the picture equally among all elements that appear at each step.

Using the result that (1 + x 2 m )  (1 + x) 2 m modulo 2 for any m , one then finds that the repetition period always divides the quantity p[n]=2^MultiplicativeOrder[2, n] - 1 , which in turn is at most 2 n-1 -1 . … And now the repetition period for odd n divides q[n]=2^MultiplicativeOrder[2, n, {1,-1}] - 1 The exponent here always lies between Log[k, n] and (n-1)/2 , with the upper bound being attained only if n is prime.

The table below gives the digit sequences for several rational numbers obtained by dividing pairs of whole numbers.

A typical feature is that the patterns are divided into several separate regions, often emanating from some kind of center.

And to emulate a mobile automaton with a cellular automaton it turns out that all one need do is to divide the possible colors of cells in the cellular automaton into two sets: lighter ones that correspond to ordinary cells in the mobile automaton, and darker ones that correspond to active cells.