A previous booklet, Life 's Still Lifes, presented an algorithm capable of revealing all Life forms of the type (m,n,t), which move uniformly m cells in the x-direction and n cells in the y-direction after t generations. Strictly speaking, the algorithm only yields those forms which can be found in strips of finite width or, which are spatially periodic. Although finding all the forms which could fill the whole plane without periodicity is an undecidable proposition, with ingenuity many other interesting forms can nevertheless be found. However, that is another story.
Life possesses the characteristic that many of its forms are surrounded by arbitrarily long quiescent stretches, which makes them freestanding. The same algorithm yields all isolated forms of this nature. In either event the amount of computation required to obtain forms of even modest extent is quite considerable. Forms of long period, likewise all those of period two, are inaccessible to present computer power. Consequently this presentation is limited to forms whose characteristics can be ascertained within a single generation.
Still lifes, creepers and crawlers can be determined; the latter are not gliders because they are not freestanding; rather many are fuses whose quiescent surroundings extend infinitely in only one direction. Nor do they move by reflection and translation. Still, the word ``glider'' has acquired a generic connotation referring to any moving configuration and is often used where it is not strictly appropriate.
The algorithm involves two stages of de Bruijn diagrams. The first stage diagrams have a maximum of 64 nodes, typically with four links each, except those which do not belong to the ergodic set of the diagram; those often have none, or participate in chains leading to end nodes which have no continuation. In any event it is awkward to present the de Bruijn diagram in its preferred form as a set of chords of a circle, so a matrix form is used instead.
Even the matrix presentation is unwieldy, so the style actually adopted consists of listing the nodes of the ergodic set on a line together with the nodes to which they are linked. Each line will have a maximum length determined by the number of outgoing links in the full de Bruijn diagram, which in turn will be a fraction of the length of the rows of the full connectivity diagram.
Having formed the first stage de Bruijn diagram, the second stage can be constructed. All the loops in the first stage with a chosen length are candidates to be links in the second stage diagram, that length now becoming the width of a periodic strip. Again, links will be discarded for not joining nodes within the ergodic set.
The following sections are laid out according to the behavior that can be discerned after a single generation of evolution, that is, still lifes, followed by longitudinal, transversal, and diagonal gliders. Only one instance of each symmetry class is presented, meaning that further patterns can be gotten by planar rotations or reflections of the ones shown. The list could also be extended by exhibiting the precursors of a completely quiescent field, or of a completely live field; but all such results have been omitted for reasons of space.
Likewise six is the maximum width of the periodic strips shown; diagrams for wider strips would not fit on a single page without some change in the style of presentation. Since the strips are periodic, they are subject to further reflective and rotational symmetries; the tables have been further compressed by showing only symmetry classes. Link superscripts such as L, R, rot, or F imply that the next node is to be rotated to the left, right, arbitrarily, or reflected, before continuing. Only one node of any given symmetry class is shown.