Volume two

With JavaScript on, choose a section to see its entries, grown from their seeds. Without it, every section and its note stands below.

1. Growing seeds78 entries

   Seeds that never stop: the opposite of the ornaments. Gems are crystals that grow under direction order from as few as 4 tiles, faceted like cut stones, until they fill the board; 513 of the 902 direction-order rules grow one, in 209 distinct cuts, and the 30 most common are here. Starbursts and garlands draw outward forever in the 16-neighbour Lines and Woven rules; garlands only ever appear in the Lines rule. Kaleidoscope, pinwheel and Rorschach fires are the wildfire rule started from symmetric seeds, and fireworks throw symmetric showers of gliders. No seed under the default rule ever does this.

2. Glyphs144 entries

   Small seeds with a single mirror that settle into one compact piece with enclosed spaces, like a letter, a sign or a mask. A script for nuna: 72 from the default rule, 36 bolder ones from Island and 36 more letter-like ones from Both fail, chosen from about 35,000 found.

3. Echoes50 entries

   Ornaments redrawn 2 to 5 times larger and handed to the rule. A big solid shape is overcrowded, so the rule thins it to the parts that hold, the way it keeps the edges of a photo; what settles is the same ornament at a larger size with new fine detail. The formula: draw the outline larger, fill it with tiles that keep each original tile’s direction and the ornament’s symmetry, try four fills, and keep whichever settled result looks most like the original. Doubling in 2× steps beats one big jump: Four crowns doubled twice scores 0.95 at 4×, and a third doubling reaches 8× (4,644 tiles, too large for this page) at 0.93. Likeness is measured from mid-distance; 1.00 would be identical.

4. Cloths that scale65 entries

   Swatches from the swatch book redrawn 2×, 3× and 4× larger on a repeating cell: the same cloth at several gauges. 104 settle into a new repeat that still looks like the original, 14 survive to 4×, and six keep their response to a missing tile at both 2× and 3×. Under Both fail nearly every cloth scales, because that rule freezes whatever it is given; under Island almost none do, because it fills cloth in.

5. Living cloths53 entries

   Repeating patterns that never stop moving, from four rules. The liveliest change half their places over each beat; the slowest, an Island cloth, takes 40 generations to come round, passing through dots, bars, stripes and hearts. A few travel: the whole cloth slides along, up to one and a half places a generation, like a moving pattern on a screen. Most moving cloths stay in place, and some flip between two half-shifted states.

6. Breathers and pulses30 entries

   Oscillators that grow from a single combination shape and keep returning to it, among them the breather: four tiles that bloom to thirty and come back every 41 generations. In Conway’s Life oscillators are the clocks of every machine; here they are motion pixels, marks that pulse at their own tempo.

7. Pulsing ornaments87 entries

   Symmetric ornaments that settle into a steady beat instead of holding still. None is a phoenix, where every tile changes each step: at least two-thirds of each stays put, a still frame (Life’s stator) around a moving heart (its rotor). The most restless, with up to a third of themselves moving, are named Restless ornament.

8. Combination groupings180 entries

   A combination shape copied eight ways around a centre, so the copies meet and negotiate. Life builds its machines by colliding known pieces (glider synthesis); these are the nuna version, named by the shape that made them.

9. Labyrinth ornaments120 entries

   The Labyrinth rule as a material: dense, rounded medallions.

10. Woven ornaments80 entries

    The woven-lines rule as a material: pens draw parts of the ornament as straight lines, so many come out as line drawings already.

11. Lines ornaments60 entries

    The Lines-and-wanderers rule as a material: chunky and bold.

12. Masks70 entries

    Mirror-symmetric seeds under the default rule: faces, masks and totems.

13. Giants94 entries

    The largest ornaments: tiers grown ring by ring around the named families, up to a fifth tier of 5,456 tiles whose centre survived every tier unchanged, like growth rings, and seeds twice the usual size. In Life the biggest settled patterns come from methuselahs.

14. Negotiated wallpapers8 entries

    The same seed planted on a grid, close enough that neighbours collide as they grow. They settle their borders into a repeat, like Conway’s agars, the patterns that fill the whole plane. Mixed seeds never agree, and keep boiling.

15. Island, turning50 entries

    The Island rule grown from turning seeds: bold pinwheels.

16. Both fail, 4-way mirror60 entries

    Default counts with both fail, grown from 4-way mirror seeds: crisp, lacy and balanced.

17. Transplants176 entries

    Finished volume-one ornaments used as seeds under a different rule, so the same piece is regrown in a new material. Life calls rules other than Conway’s Life-like; here a rule is a material.

18. Second-generation crosses80 entries

    The inside of one seed joined to the outside of another, where at least one parent was itself a cross: breeding, the way Life enthusiasts grow new patterns from old ones.

19. Crosses in other materials120 entries

    Seed crosses made within the Island, Both fail and Labyrinth rules, from those rules’ own ornaments.

20. Pulsing crosses60 entries

    Crosses of two seeds (the inside of one joined to the outside of another) that settle into a beat rather than holding still, from the default and Labyrinth rules.

21. Mutations125 entries

    Volume-one ornaments with one symmetric group of tiles taken away, left to regrow. About one time in six they heal back exactly; otherwise they settle into a close variant, like an alternate form of a letter.

22. Duets44 entries

    Two different named ornaments set edge to edge and left to negotiate where they touch. 44 of the 78 possible pairs settled into something new.

23. Ornament wallpapers81 entries

    A finished ornament repeated edge to edge in a square grid or a half-drop, so neighbours touch on every side and negotiate their borders. Many grow linking bridges and become chains, laces and trims.

24. Mutation chains78 entries

    Mutations of mutations: each family drifts one step further from its original. Second-generation variants heal slightly more often (19% against 16%).

25. The complete small set2356 entries

    Every ornament that an 8-way symmetric seed fitting inside a radius of 5 places can grow: a closed alphabet for each rule. Default: 582 shapes (542 still, 40 pulsing), from 807,443 seeds, the last 177,000 finding nothing new. Labyrinth: 939, the richest and the liveliest, with 164 pulsing. Both fail: 688. Island: only 147, bold and rounded. Seeds just a little larger open the space up enormously. Under the default rule the count grows about tenfold for every extra place of radius: about 11,000 at radius 6, 109,000 at 7, 840,000 at 8, and over 3.6 million at 12, where almost every seed grows something never seen before.

Checked

• Every entry with a seed (4,142 of 4,349) was regrown with the nuna life engine when these pages were built. 4,081 matched their recorded form tile for tile and 27 settled into the recorded beat; 34 did not match (V2-0385, V2-0398, V2-0419, V2-0452, V2-0576, V2-1448, V2-1458, V2-1464, V2-1480, V2-1482, V2-1484, V2-1501, V2-1503, V2-1504, V2-1505, V2-1508, V2-1510, V2-1517, V2-1519, V2-1521, V2-1536, V2-1654, V2-1658, V2-1661, V2-1664, V2-1695, V2-1697, V2-1699, V2-1705, V2-1713, V2-1720, V2-1721, V2-1723, V2-1744), and their cards show the recorded form. The 207 cloths are recorded as repeats and have no seed.
• A seed that never settles is shown at the generation the volume recorded.
• Game codes: 4,112 are rebuilt from rule and settled tiles and equal the volume's own; the other 237 (207 cloth codes and 30 more) are carried exactly as the volume records them.
• Each section's data is its own file, loaded when the section is opened; finding by id or name loads one index file.