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The black dots indicate all the cells that change.
A dot shows at which step a given string first appears—and indicates the shortest proof of the theorem that string represents.
The resulting evolution process is likely to have attractors, potentially explaining the fact that in images such as "Magic Eye" random dot stereograms features can pop out after several seconds or minutes of scrutiny, even without any conscious effort.
For while it is easy to tell that a cave painting of an animal is a piece of purposeful art, dots carved into a rock in an approximate rule 30 pattern might not even be noticed as something of human origin.
Away from these extreme cases, rapid convergence is seen to a spacing between black dots of almost exactly 137.5°.
The picture demonstrates that dots which are initially close together rapidly separate.
Successive black dots indicate where the planets are on each revolution of the stars.
The black dot, representing the location of a crack, moves from one cell to another based on the displacements of neighboring cells, at each step setting the cell it reaches to be white.
Picture (a) is a version of the standard representation that I have used for mobile automaton evolution elsewhere in the book—in which successive lines give the colors of cells on successive steps, and the position of the active cell is indicated at each step by a gray dot.
Only the dots are significant; the shading and lines between them are just included to make the plot easier to read.