RAM [emulated with cellular automata] The rules for the cellular automaton shown here are {{2, 4 | 8, 2 | 11, _, _}  2, {11 | 10, 4 | 8, 2 | 11, _, _}  11, {2, 4 | 8, _, _, _}  10, {11 | 10, 4 | 8, _, _, _}  2, {2, 0, _, _, _}  2, {11, 0, _, _, _}  11, {3 | 7 | 6, _, 10, _, _}  1, {x : (3 | 7 | 6), _, _, _, _}  x, {_, _, 6, 4, 10}  5, {_, _, 6, 8, 10}  9, {_, 3, _, 10, _}  4, {_, 7, _, 10, _}  8, {_, _, 1, _, x : (5 | 9)}  x, {1, _, _, _, _}  1, {_, _, 1, _, _}  1, {_, _, _, _, 1}  1, {_, _, x : (4 | 8 | 0), _, _}  x} The initial conditions are divided into two parts: instructions on the left and memory on the right.

Locally isotropic growth A convenient way to see what happens if elements of a surface grow isotropically is to divide the surface into a collection of very small circles, and then to expand the circle at each point by a factor h[x, y] .

The total number of configurations in rule 90 that repeat with any period that divides p is always 4 p . … The total number of configurations in rule 30 that repeat with periods that divide 1 through 10 are {3, 3, 15, 10, 8, 99, 18, 14, 30, 163} .

what happens if one divides an image into a collection of nested squares, but imposes a lower limit on the size of these squares.

The radio spectrum from about 9 kHz to 300 GHz is divided by national and international legislation into about 460 bands designated for different purposes. And except when spread spectrum methods are used, most bands are then divided into between a few and a few thousand channels in which signals with identical structures but different frequencies are sent.

In most cases, the idea is recursively to divide data into parts, then to do operations on these parts, and finally reassemble the results.

Among such computations are Plus , Times , Divide , Det and LinearSolve for integers, as well as determining outcomes in additive cellular automata (see page 609 ).

One is the almost-straight 30-mile railroad causeway built in 1959 that divides halves of the Great Salt Lake in Utah where the water is colored blue and orange.

It has arisen in many different guises and been useful in proving theorems in many areas of mathematics, but it has seemingly peculiar consequences such as the Banach–Tarski result that a solid sphere can be divided into six pieces (each a non-measurable set) that can be reassembled into a solid sphere twice the size.

The spectrum is roughly like the markings on a ruler that is recursively divided into {GoldenRatio, 1} pieces.