Three Closer Views of Life
Cellular automata are usually rendered in a stark, clear monocolor for ease of computation. There are however many different ways to visualize any given one, which can show more detail of what’s going on in a pattern. This will probably be particularly illustrativ when animation or actual computation cannot be used.
I follow here the evolution of a famous Life pattern — the R-Pentomino, which continues to evolve for an unusually long time before settling down — in three custom visualizations I’ve created for various uses. (This functionality is supported by the excellent Life program Golly.) The three series of snapshots are taken at generations 10, 100 and 1000.
The left column simply highlights what kind of environment each cell has. As in all three visualizations, isolated empty space is pure black. Live cells come in nine different colors however:
- Cells dying from underpopulation — with 0 or 1 neighbors — are in shades of cyan, casting electric sparks along decaying fringes.
- Cells that will survive — with 2 or 3 neighbors — are in white and pale yellow, shining bright as zones of stability.
- Cells dying from overpopulation — with 4+ neighbors — are in shades of orange, red and magenta, showing where growth has overheated and must restart.
Dead cells near the pattern have their color-code as well.
- Gray cells have 1 to 2 live neighbors, marking empty space that is just barely within the pattern’s area of influence.
- Green cells have 3 neighbors, marking spots where new live cells will be born in the next generation.
- Blue cells have 4+ neighbors, marking the nooks and holes in the pattern, most of them resulting from died-out interior cells.
The center column adds a deeper time dimension to the pattern: newborn cells are shown in white, while as they age, live cells pass thru yellow, orange, red, purple, and finally reaching a deep blue at a respectable 8 generations of age. Currently active areas of a pattern are thus easy to tell apart from the stabilized remnants of older activity. This also highlights asymmetries in the ways different shapes have evolved. For example, the symmetric oblong ellipsoid shape near the center reveals how its oldest parts are the four “teeth” at the center, particularly the northeastern one. Or, in the last snapshot, you can see how one of the 2×2 blocks was recently created and is still “cooling down”.
The right column finally keeps track of the entire timeline of the pattern. All locations where live cells have occurred, thus far, are marked as blue; a darker blue fringe again marks cells of empty space that have been under the pattern’s “influence” (i.e. marking the territory near which other patterns could not be placed without being perturbed at some point). Thus, the overall history of forward shoots and former explosions still casts a shadow.
Particularly noticable are the long highways at the last stage, left behind by the gliders emitted from the pattern. The first one of these (which, incidentally, is also the first glider that was ever seen in studies of Life) can already be seen at the second stage, heading southeast towards infinity.
(This visualization would also highlight in various ways cells that have survived intact from the beginning; none of that to be found here, however…)
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