List of Figures

• A sample of evolution according to Rule 110.  
• Some slight variants on Rule 110, according to the retention of the upper left corner of triangles, and likewise whether the bottom vertex is closed off or not.  
• A (2,2) rule with characteristics similar to (2,1) Rule 110.  
• Format of the tiles appearing in the evolution of Rule 110, as it affects the appearance of the T3 tile.  
• The plane tiled by T1 triangles.  
• The plane tiled by T2 triangles. Left: alpha phase, in which the triangles are stacked diagonally. Right: beta phase, in which they are stacked in columns.  
• The plane tiled by T3 triangles. Left: alpha phase, in which the triangles are stacked diagonally with slope -1/2 in periodic rectangular tiles 7x14. Right: preferred ethereal beta phase, in which they are stacked diagonally with slope -2 in periodic rectangular tiles 14x7. The beta phase welcomes intercalcated T1's, whereas the alpha phase does not,  
• The locations of Cook's gliders relative to the ether lattice. The two barred gliders sit lower on the same velocity lines as the unbarred gliders. Small circles on the T3 mosaic show possible positions of compatible gliders, but they could be impossible, duplicates, or so far undiscovered.  
• To tile the plane, T4 triangles can be stacked diagonally, an arrangement which is compatible with the T1 lattice. Otherwise they have to be paired with some other, smaller, triangle such as a T1 diagonally situated. Once triangles of disparate sizes occupy a unit cell, many combinations still having similar areas are possible.  
• To tile the plane, T5 triangles cannot be stacked diagonally, unless they are placed slightly off center. There remain interstices which can be filled by one or two T1 tiles, but not by two T1's in a row if Rule 110's evolution is to be respected.  
• Samples of left shifting configurations. The quiescent configuration is an implicit component of every other shift; sometimes it is the only one. Otherwise it is not shown. When there are still more components, the panel is split into horizontal slices to accomodate them.  
• Periodic configurations. The quiescent configuration is an implicit component of every other shift; sometimes it is the only one. Otherwise it is not shown. When there are still more components, the panel is split into horizontal slices to accomodate them. That is not the same as a one-sided ideal, in which one single panel divides into two distinctive regions along a vertical fissure.  
• Samples of right shifting configurations. The horizontal coordinate determines the shift, the vertical coordinate the number of generations which have elapsed.

  The quiescent configuration is an implicit component of every other shift; sometimes it is the only one. Otherwise it is not shown.  

• Subset diagram for Rule 110.The shortest excluded word is 01010.  
• Mean field probability distributions for the first five generations of evolution of Rule 110. The uniform 50% distribution tends toward superstability.  
• Two-block probabilities, showing a linear (rather than quadratic) relation valid at low densities, slope 1/2, holding over an extensive range.  
• There are three species of composite tile from which gliders of velocity 2/5 c arise.  
• Reading left to right, the T1 tiles can be repeated until they meet a T3, following which T3's and T5's may repeat or alternate arbitrarily.  
• The de Bruijn diagram provides the only satisfactory description of the interrelation between the three species.  
• One species moves 4 left every six generations against a background generated by the other.  
• The second species is the glider, moving against a background established by the first.  
• The first species is the glider, moving against a background established by the second.  
• One species moves 4 left every six generations against a background generated by the other.  
• One species moves 1 left every six generations against a background generated by the other.  
• The second species is the glider, moving against a background established by the first.  
• The first species is the glider, moving against a background established by the second.  
• One species moves 1 left every six generations against a background generated by the other.  
• T1 based gliders, showing the four ways that they may seem to be attached to the ether tile. Strings of T1's running diagonally downwards are quite conspicuous, and a very common form of glider.  
• Thicker gliders with two, three, and four diagonals of T1's.  
• Turn about is fair play. T3's can appear to be gliders when displayed against a T1 background.  
• Cook's A-gliders and the de Bruijn diagram from which they may be derived. The outer periphery corresponds to the period-7, cycle 14 period rectangle of the ether tiles. If T3's and T1's alternate, there are three phases each of which has a cycle length of 6. Also, if pure T1's run in succession, there is a loop of length 4 which will geberate them. Other mixtures correspond to other paths through the diagram.  
• The only (4,6) gliders seem to be those already inmplicit in (2,3): the A-gliders.  
• T1 based gliders. However, T1 tiles cannot be juxtaposed as they can in the A gliders.  
• Cook's B-gliders and the de Bruijn diagram from which they may be derived. The outer periphery corresponds to the period-7, cycle 14 period rectangle of the ether tiles. If T3's and T1's alternate, there are three phases each of which has a cycle length of 6.  
• B-bar gliders have the same velocity as B gliders, but take three times as long to develop their cycle; however the two types, B and B-bar, may coexist.  
• B-bar gliders can have varying widths and one or the other of two optional right margins.  
• T6 based gliders, which actually don't move.  
• Sequence diagram for the tiles in C gliders.  
• Cook's C-gliders and the de Bruijn diagram from which they may be derived. [Zero removed]  
• T4 based gliders, which move slowly right.  
• There are two kinds of D gliders, each slightly different.  
• T8 based gliders, which move leisurely leftwards.  
• A swatch of E glider.  
• The E-bar glider has the same velocity as E gliders, but it takes twice as long to complete its period. Two periods of the E-bar are shown, to better to see how it fits in with the ether tiles.  
• The lackadasical F glider, which moves 4 left in 36 generations, for a velocity of -1/9 c.  
• Gliders based on a mixture of T5, T6, T8 and smaller ones, which move left at 1/3 light velocity.  
• The G glider is extensible by the same mechanism which extends E gliders, with the difference that alternative tiles are used which gives proportional spacing between the T5 chains.  
• The H glider, is indeed rather large and complicated, moving left 18 cells in 92 generations, about -c/5.  
• The glider gun glides, and having glided, glides on.  
• A and B gliders, travelling in opposite directions, can collide. They leave no trace of their former existence.  
• A and C gliders, colliding just right, transform into an F.  
• One of the reasons that large triangles do not occur often in evolutions is that they do not pack well.