The pictures at the top show the first hundred steps in evolution according to various rules starting from a pair of black elements. … Note that in case (c), all the elements are eventually removed from the sequence.

So even though the total of the energy of all particles remains the same, the distribution of this energy becomes progressively more random, just as the usual Second Law implies. … In the top group of pictures, the particles bounce around in an empty square box. … In the top group of pictures, the arrangement of particles shows simple repetitive behavior.

For purposes of display the ring of active material is unrolled into a line, and successive states of this line are shown one on top of each other going up the page. … In the extreme case where all memory of previous behavior is immediately damped out the first picture at the top of the facing page shows that successive elements form at 180° angles. … The concentration of a chemical is indicated by gray level, and for the top line at each step, it is also plotted.

The programs for each of the machines are given at the top, with ► representing an increment instruction, and ◄ a decrement-jump. … All the register machines shown start by executing the first instruction in their programs. … Each machine follows a fixed program given at the top.

In the first case, however, the black walls that are present seem to prevent any long-range transmission of information at all. … The pictures at the top of the next page give some indication of how this might be done. … The top example uses completely random initial conditions; the bottom example uses initial conditions in which no run of an even number of black squares ever occurs.

Symmetric 5-neighbor [2D cellular automaton] rules Among the 32 possible 5-cell neighborhoods shown for example on page 941 there are 12 classes related by symmetries, given by s = {{1}, {2, 3, 9, 17}, {4, 10, 19, 25}, {5}, {6, 7, 13, 21}, {8, 14, 23, 29}, {11, 18}, {12, 20, 26, 27}, {15, 22}, {16, 24, 30, 31}, {28}, {32}} Completely symmetric 5-neighbor rules can be numbered from 0 to 4095, with each digit specifying the new color of the cell for each of these symmetry classes of neighborhoods.

The pictures at the top of the next page show four different rules that each have the property that if started from initial conditions in which all possible sequences of cells are allowed, these same sequences can all still occur at any subsequent step in the evolution. … What is going on, however, is that in a sense the particular initial conditions that allow all possible sequences are special for these rules.

The pictures at the top above are obtained by keeping only the steps indicated by arrows on the left. … The pictures at the top above are obtained by keeping only the steps indicated by arrows on the left.

And still others may cause regions of tissue to die—thereby for example allowing separate fingers and toes to emerge from a single sheet of tissue. … And what has been discovered in the past decade or so is that in all animals—as well as plants—there are a handful of so-called homeobox genes which seem to become active or inactive at particular concentration levels and which control what section of the underlying genetic program will be used.

And for example particularly in lower animals there are all sorts of cases where very simple and predictable responses to stimuli are seen. … Indeed, as a practical matter what usually seems to happen is that we receive external input that leads to some train of thought which continues for a while, but then dies out until we get