Patterns · Ornaments
An ornament is where a nuna life rule comes to rest. A few seed tiles go in, the rule decides everything after, and what is left when the growth stops, or settles into a steady beat, is the ornament. Nothing on these pages is drawn by hand; every piece was found by growing a seed.
nuna life is the Game of Life played with nuna tiles. Each generation, a tile stays if the number of tiles touching it is on the rule's stays list, and a tile is born in an empty place whose count is on its born list. The rule treats every direction alike, so a symmetric seed can only grow a symmetric shape: an 8-way seed grows an 8-way ornament, a single mirror grows a face or a letter, a turning seed grows a pinwheel.
Most growth ends. A seed churns for a few generations or, in volume one, as many as 2,421, then stops, or settles into a steady beat. That resting form is the ornament. Because the rule decides everything after the seed, each ornament is the only thing its tiles could have become: to make something new, change the seed or change the rule, never the result.
Ornaments come in families. A ring of new seed tiles round a settled ornament grows the next tier of its family; the inside of one seed with the outside of another breeds a cross; damage one and it heals or becomes a close variant. These pages keep those relations: volume one is arranged by family and tier.
The same seed grown under another rule is the same idea in another material. Default is stone; Both fail is lace cut in stone; Island is bold and round, and Labyrinth dense. Lace blooms, Woven draws lines and Lines is chunky; Traffic moves, Wildfire never stops, and direction order cuts gems. So a rule never disqualifies a pattern: it gives it a material.
Volume one uses four rules:
| Rule | What it does | Token | Ornaments |
|---|---|---|---|
| Default | 24 neighbours · born 3, 4 · stays 2, 3, 4 · more neighbours wins | 24-34-234-m | 1,440 |
| Both fail | 24 neighbours · born 3, 4 · stays 2, 3, 4 · both fail | 24-34-234-f | 165 |
| Island | 24 neighbours · born 2, 3, 4 · stays 3, 4, 5 · more neighbours wins | 24-234-345-m | 150 |
| Lace | 16 neighbours · born 2 · stays 1, 2 · more neighbours wins | 16-2-12-m | 73 |
Volume two uses 44 rules, among them the 16-neighbour rules (only tiles sharing a curved edge count as neighbours) and the direction-order rules, where a contested birth goes to the first direction in the order down, right, up, left. Each piece's own rule is written out on its page.
Nuna ornaments, volume one · 1,828 ornaments, 568 families. Ornaments grown under four rules from symmetric seeds, grouped by family: each family is a base ornament and the larger ornaments grown from it, tier by tier (a ring of new seed tiles round the settled ornament, grown again by the same rule), plus crosses (the inside of one seed joined to the outside of another).
nuna ornaments 2 · 4,349 entries, 25 sections. Everything that grew out of the NUNALAB search rounds, in 25 sections: growing seeds, glyphs, echoes, cloths, pulsing ornaments, other materials, giants, transplants, crosses, mutations, duets, wallpapers and the complete small set. Each section's note says what it found.
An alphabet is every ornament one kind of seed can grow under one rule. These were found by growing every seed once, not by sampling, so each one is closed: within its seed definition there is no other ornament to find. The alphabets page says exactly what that covers and what it doesn't.
| Radius | Rule | Seeds | Ornaments | Still | Pulsing | Seeds that die |
|---|---|---|---|---|---|---|
| 5 | Default | 2,119 | 572 | 542 | 30 | 461 |
| 5 | Labyrinth | 2,119 | 897 | 795 | 102 | 28 |
| 5 | Both fail | 2,119 | 686 | 677 | 9 | 429 |
| 5 | Island | 2,119 | 141 | 124 | 17 | 1,616 |
| 6 | Default | 96,242 | 11,786 | 11,052 | 734 | 11,883 |
| 6 | Labyrinth | 96,242 | 24,103 | 20,975 | 3,128 | 253 |
| 6 | Both fail | 96,242 | 17,661 | 17,562 | 99 | 11,870 |
| 6 | Island | 96,242 | 2,460 | 1,746 | 714 | 62,148 |
| 7 | Default | 5,298,236 | 377,560 | 350,382 | 27,178 | 379,791 |
What nuna life has found, filed so it can be sorted and carried into future projects. Every entry has a kind, tags, the rules it concerns, examples by reference into the volumes, and the kinds of project it carries to.
Entries NL-077, NL-078, NL-079, NL-080 come from the Patterns tab's enumerations. A correction is a new entry that names the one it corrects; the older entries stand as written.
NL-001 · foundation · foundation, lattice
Every place on a square lattice is a circle when x + y is even and a diamond when it is odd. A tile is one circle fused to one orthogonally adjacent diamond, so it points one of four ways: 0 diamond below, 1 right, 2 above, 3 left. Boards wrap at their edges.
every nuna project
nuna life
NL-002 · foundation · foundation, neighbourhood, badge
A tile counts its neighbours among the places of a badge laid round it: the 24-point badge by default, the 16-point badge by deliberate choice. The badge is the same geometry as the 16- and 24-point badges of the nuna system, used as a sense of touch.
Aaron: 24 everywhere; 16 only when deliberately chosen.
Patterns tab · keypad · clock
nuna life
NL-003 · foundation · foundation, rule, contest
Rules are written like Life's B/S notation with two additions: which badge counts (24 or 16), and what happens when several births claim the same place (the contest): more neighbours wins, both fail, or direction order.
Default: 24 neighbours, born with 3 or 4, stays with 2 to 4, more neighbours wins.
default
Patterns tab
nuna life
NL-004 · foundation · foundation, code, interchange
Any piece travels as a game code: nuna2.<rule>.<tiles> for a shape, nuna2c.<rule>.<w>x<h>.<cells> for a cloth. Tiles are base64 byte triples (x+128, y+128, direction). Codes open in every nuna life edition, both ornament books, nuna space life and its puzzle maker.
every nuna project
nuna life
NL-005 · material · material, rule
Born 3 or 4, stays 2 to 4, more neighbours wins, 24 neighbours. Brings nearly every seed to rest as a still ornament. No gliders have been found under it, and no seed under it grows for ever. Aaron's favourite rule.
the 13 named families, 1,440 of volume one's 1,828 ornaments
default
V1-0001 · V1-0006
Patterns tab · textiles
nuna life
NL-006 · material · material, rule
Default counts, but a place two births contest stays empty. Crisp, lacy, balanced ornaments, especially from 4-way mirror seeds.
165 in volume one; 830 entries in volume two
fail24
Patterns tab · textiles
nuna life
NL-007 · material · material, rule
24 neighbours, born 2 to 4, stays 3 to 5. Bold pinwheels from turning seeds. Its slowest living cloth takes 40 generations to come round, through dots, bars, stripes and hearts.
150 in volume one
island
Patterns tab · textiles
nuna life
NL-008 · material · material, rule
24 neighbours, born 3 or 5, stays 1 to 4. Dense, rounded medallions; its small still shapes make battlements.
1,238 entries in volume two
laby
Patterns tab · textiles
nuna life
NL-009 · material · material, rule
16 neighbours, born 2, stays 1 or 2. Lifting one tile and handing a shape to Lace makes it bloom 1.5 to 3.5 times its width and settle in 14 to 50 generations: an explosion made by the rule. The breather lives here: four tiles that bloom to thirty and return every 41 generations.
73 in volume one; the explosion rule of every nuna game
d16
Patterns tab · textiles
nuna life
NL-010 · material · material, rule
16 neighbours, born 2, stays 2 or 3. Pens draw parts of an ornament as straight lines, so many come out as line drawings already. Starbursts draw outward for ever.
80 woven ornaments in volume two
woven
Patterns tab · textiles
nuna life
NL-011 · material · material, rule
16 neighbours, born 1 or 2, stays 2 or 3. Chunky, bold ornaments. Garlands, beaded chains that grow along one axis, appear only under this rule.
60 Lines ornaments
lines
Patterns tab · textiles
nuna life
NL-012 · material · material, rule
16 neighbours, born 2 or 4, stays 2 or 3. Home of gliders: a fast diagonal one with period 4, a straight one that moves 12 places in 34 generations. Still shapes up to 88 tiles hold under it.
traffic
Patterns tab · textiles
nuna life
NL-013 · material · material, rule
16 neighbours, born 2 or 3, stays 1 or 2. Symmetric seeds start fires that spread for ever: kaleidoscope, pinwheel and Rorschach fires. Still shapes up to 124 tiles hold under it.
fire
Patterns tab · textiles
nuna life
NL-014 · material · material, rule
When births are settled by direction order, many rules grow gems: crystals from as few as 4 tiles, faceted like cut stones, until they fill the board.
513 of the 902 direction-order rules grow a gem, in 209 distinct cuts
dir
Patterns tab · textiles
nuna life
NL-015 · law · symmetry, seed, ornament, method
The rules are symmetric, so a symmetric seed can only grow a symmetric shape. Seeds with 8-way, 4-way, mirror or turning symmetry grow ornaments with the same symmetry. This is the method behind the most beautiful results.
Every one of volume one's 1,828 ornaments grew from a symmetric seed.
V1-0001 · V1-0008 · V1-0012
Patterns tab · textiles · print
nuna life
NL-016 · law · ornament, settling, growth
Most seeds under the default rule settle: they stop changing (still) or fall into a steady beat. The time to settle runs from a few generations to nearly a thousand.
Flower settles in 159 generations; Propeller in 926; Totem in 929.
default
V1-0006 · V1-0007 · V1-0012
Patterns tab · animation
nuna life
NL-017 · law · tier, family, growth, scale
A settled ornament with a ring of new seed tiles round it, grown again by the same rule, settles into a larger ornament of the same family. Families grow tier by tier.
Tiers up to 4 in volume one; giants up to a fifth tier of 5,456 tiles, whose centre survived every tier unchanged.
V1-0001
Patterns tab · textiles · games
nuna life
NL-018 · law · echo, scale
An ornament redrawn 2 to 5 times larger and handed back to the rule is overcrowded, so the rule thins it to the parts that hold, keeping its likeness.
Ladders of six ornaments at 1x to 5x (Four crowns: 136, 468, 1,052, 1,652 tiles).
Patterns tab · print · scale-free design
nuna life
NL-019 · law · mutation, healing, variant
Take one symmetric group of tiles from a finished ornament and let it regrow: about one time in six it heals back exactly; otherwise it settles into a close variant, like an alternate letterform.
16% heal; second-generation mutations heal slightly more often (19%).
default
Patterns tab · type design · games
nuna life
NL-020 · law · cross, breeding, seed
The inside of one seed joined to the outside of another grows a new ornament: breeding, the way Life enthusiasts grow new patterns from old.
120 crosses in volume one; second-generation crosses, crosses in other materials and pulsing crosses in volume two.
Patterns tab
nuna life
NL-021 · law · negotiation, duet, wallpaper, agar, cloth
Pieces close enough to touch negotiate their borders: two named ornaments set edge to edge settle into something new; an ornament repeated edge to edge grows bridges; a seed planted on a grid settles into a repeat, like Conway's agars.
44 of 78 duets settled into something new.
Patterns tab · textiles
nuna life
NL-022 · law · negotiation, method, verification
A field of pieces placed touching never settles, because they negotiate. With three places of room round each, a field holds still and every change can be read.
Found building nuna space life: a field with less room never settled, so finds were never read.
games · Patterns tab
nuna space life, session 2
NL-023 · law · glyph, symmetry, type
Small seeds with a single mirror settle into one compact piece with enclosed spaces, like a letter, a sign or a mask: a script for nuna.
144 glyphs in volume two.
type design · print · games
nuna life
NL-024 · law · census, alphabet, catalogue
Every ornament that an 8-way symmetric seed fitting inside a radius of five places can grow, for each rule: a finite, complete alphabet.
Default: 582 shapes (542 still, 40 pulsing). The radius-6 alphabet is nearly complete (10,165 of about 11,000).
Patterns tab · Shapes tab
nuna life
NL-025 · law · pulse, oscillator
Symmetric ornaments that settle into a beat keep most of themselves still: at least two-thirds of each holds from one step to the next.
animation · Patterns tab
nuna life
NL-026 · law · cloth, living, travelling, flaw
Repeating patterns can hold still, beat, or travel; a missing tile in one heals, scars, fuses or melts.
The liveliest living cloths change half their places each beat; travelling cloths slide up to 1.5 places a generation.
textiles · Patterns tab · animation
nuna life
NL-027 · law · cloth, gauge, scale
A swatch redrawn 2, 3 and 4 times larger on a repeating cell often settles into a new repeat that still looks like the first.
104 of the swatches settle into a recognisable new repeat (see the Cloths that scale section).
textiles
nuna life
NL-028 · law · fire, firebreak, growth
Under wildfire, an empty band three places wide stops the spread. A burned ring is a real firebreak.
fire
games
nuna space life, session 8
NL-029 · law · glider, motion, lanes
Lanes of gliders stay whole for good only if the spacing in a lane divides the board's width, and lanes flying opposite ways are at least 21 places apart. The sideways p34 glider is 13 places tall over its period. Lanes flying the same way only need not to touch.
Measured over twelve alignments and a thousand generations. An earlier claim of 12 places came from a flawed test.
traffic
games · animation
nuna space life, session 7
NL-030 · law · still, beacon, wall
Even rules that never settle hold some shapes perfectly still: under wildfire up to 124 tiles, under traffic up to 88. They make beacons to defend and walls to build.
fire · traffic
games
nuna space life, session 2
NL-031 · law · pulse, puzzle, verification
In a beating ornament the same move made a generation later is a different experiment. A puzzle's answer, found from one phase, holds only if the board is held still until the move.
Heartbeat's answer failed in play until the board was held; its lift takes 297 generations to settle into a period-2 beat.
games · Patterns tab
nuna space life, session 5
NL-032 · law · transient, methuselah, puzzle
A single lifted tile can set off a transient hundreds of generations long before anything settles.
297 generations to a beat (Heartbeat); the longest-lived single lift of one ornament lasts 145 generations (Make it last).
games · animation
nuna space life, sessions 5 and 6
NL-033 · method · fingerprint, catalogue, find
The canonical form of a shape folds all its turns and mirrors together; hashed (32-bit FNV-1a), it is the shape's identity. The nuna catalogue holds 5,050 such fingerprints, so any new settled shape can be called new to nuna, new to you, or seen.
Patterns tab · games · Shapes tab
nuna space life, session 1
NL-034 · method · lace, explosion, game
Lift the struck tile, run Lace until it repeats (at most about 46 generations), and split what's left: pieces of six or more fly on as new objects, smaller specks become sparks. Big rocks break into middle ones, and middle ones into small.
d16
games · animation
nuna life
NL-035 · method · puzzle, method, verification
Try every one-move change to a shape (every lift, every turn to a free side, every single tile placed beside it) and keep each question whose answer is one group of moves: eight or fewer, the mirror images of one move. Kinds so far: shape, vanish, beat, make it last, turn, one more, exact pulse, release.
A 168-tile ornament: 168 lifts, 296 turns, 424 placements, about 7 seconds in a browser.
games · Patterns tab
nuna space life, sessions 5 and 6
NL-036 · method · method, search
The NUNALAB rounds: random soups on big wrapping boards, rule sweeps across 24 and 16 neighbours and all three contests, patterned starts (tilings, frames, rings, cracked rows, kaleidoscopes, ornament seeds), glider collisions, gun hunts, fuses, the swatch book with flaw responses, and complete censuses. Every result is compared against Conway's vocabulary.
every nuna project
nuna life
NL-037 · method · verification, method
A count taken at an arbitrary moment can mislead: measure at the same phase each period. And a tile placed at odd x + y lands on a diamond place, where the engine silently skips it, so keep circles on circles.
The source of the glider-lanes correction.
every nuna project
nuna space life, session 7
NL-038 · method · animation, growth
Growth reads best between about 1.4 and 6 seconds, however many generations it takes, with a pause on the settled form, and looped for short pieces.
Patterns tab · animation
volumes, Oct 2026
NL-039 · idea · theory, colour, pixels
Aaron's deep-theory idea: ornaments are a kind of motion pixel symbol. In a future nuna or nuna-pixels landscape they play specialised roles, arranging and delegating colour space; watching one grow is a colour-space negotiation.
nuna pixels · Patterns tab
Aaron
NL-040 · idea · Patterns tab, rule
For the Patterns tab: rules should not rule out large sections of interesting patterns. Change the rule instead, or give the changed rule its own section.
Patterns tab
Aaron
NL-041 · idea · cloth, living, Patterns tab
The Patterns tab's next phase: patterns that move and answer damage. Living and travelling cloths, gauges, and the swatch book's flaw responses (heals, scar, fuse, melts), beside the static coverings.
Patterns tab · textiles
Patterns tab brief, Oct 2
NL-042 · idea · textile, cloth
Swatches and gauges are fabric repeats. Living cloths are animated textiles, and flaw responses describe how a weave behaves when a thread is pulled.
textiles · bandanas · Pendleton
nuna life
NL-043 · idea · type, print, glyph
Glyphs read as a script; ornaments, drawn as true shapes (silhouette, outline), are print and laser motifs.
print · laser cutting · Shapes tab
nuna life
NL-044 · idea · game, protect
A family of games where one ornament holds still under the board's own rule and the rule attacks it: fire (Firebreak), gliders (Siege), falling stone (Meteors). It grows a tier each time it is kept (nuna keeper).
games
nuna space life and nuna keeper, sessions 8 and 9
NL-045 · idea · sound
Births near the player as soft high notes and deaths as lower ones, on a pentatonic scale for each rule, with a drone on the rule's root.
sound · games
nuna space life, session 3
NL-046 · idea · Shapes tab, combination shapes
Aaron wants each combination shape's nuna life behaviour added as index data to the full shapes catalogue.
Shapes tab
Aaron
NL-047 · open question · metatile, glider, open
Life's OTCA metapixel builds Life inside Life. A nuna equivalent needs glider guns, splitters and turners that hand back the same glider. Right-angle turners exist; chaining two has not yet worked; no gun or splitter has been found.
research
nuna life
NL-048 · open question · census, open
The radius-6 alphabet is nearly complete (10,165 of about 11,000); radius 7 and beyond are too large to finish and can only be sampled for favourites.
research
nuna life
NL-049 · open question · echo, gauge, glyph, open
Echoes of more ornaments; cloth gauges in other rules; glyph sets at other symmetries.
research · Patterns tab
nuna life
NL-050 · open question · badge, neighbourhood, open
A possible 40-point badge as a larger neighbourhood: what rules make good ornaments with it?
research
nuna life
NL-051 · open question · open, applications
Conway's Life found uses beyond itself (computation, art, music, biology models). Which of these does nuna life suit?
research
nuna life
NL-052 · volume note · volume two, growing
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.
Patterns tab
nuna ornaments 2
NL-053 · volume note · volume two, glyphs
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.
Patterns tab
nuna ornaments 2
NL-054 · volume note · volume two, echoes
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.
Patterns tab
nuna ornaments 2
NL-055 · volume note · volume two, scalecloth
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.
Patterns tab
nuna ornaments 2
NL-056 · volume note · volume two, living
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.
Patterns tab
nuna ornaments 2
NL-057 · volume note · volume two, pulse
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.
Patterns tab
nuna ornaments 2
NL-058 · volume note · volume two, pulsing
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.
Patterns tab
nuna ornaments 2
NL-059 · volume note · volume two, groups
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.
Patterns tab
nuna ornaments 2
NL-060 · volume note · volume two, laby
The Labyrinth rule as a material: dense, rounded medallions.
Patterns tab
nuna ornaments 2
NL-061 · volume note · volume two, woven
The woven-lines rule as a material: pens draw parts of the ornament as straight lines, so many come out as line drawings already.
Patterns tab
nuna ornaments 2
NL-062 · volume note · volume two, lines
The Lines-and-wanderers rule as a material: chunky and bold.
Patterns tab
nuna ornaments 2
NL-063 · volume note · volume two, masks
Mirror-symmetric seeds under the default rule: faces, masks and totems.
Patterns tab
nuna ornaments 2
NL-064 · volume note · volume two, giants
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.
Patterns tab
nuna ornaments 2
NL-065 · volume note · volume two, walls
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.
Patterns tab
nuna ornaments 2
NL-066 · volume note · volume two, island_turn
The Island rule grown from turning seeds: bold pinwheels.
Patterns tab
nuna ornaments 2
NL-067 · volume note · volume two, fail_mirror
Default counts with both fail, grown from 4-way mirror seeds: crisp, lacy and balanced.
Patterns tab
nuna ornaments 2
NL-068 · volume note · volume two, transplants
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.
Patterns tab
nuna ornaments 2
NL-069 · volume note · volume two, cross2
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.
Patterns tab
nuna ornaments 2
NL-070 · volume note · volume two, crossmat
Seed crosses made within the Island, Both fail and Labyrinth rules, from those rules’ own ornaments.
Patterns tab
nuna ornaments 2
NL-071 · volume note · volume two, pulsecross
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.
Patterns tab
nuna ornaments 2
NL-072 · volume note · volume two, mutations
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.
Patterns tab
nuna ornaments 2
NL-073 · volume note · volume two, duets
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.
Patterns tab
nuna ornaments 2
NL-074 · volume note · volume two, ornwalls
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.
Patterns tab
nuna ornaments 2
NL-075 · volume note · volume two, mutchains
Mutations of mutations: each family drifts one step further from its original. Second-generation variants heal slightly more often (19% against 16%).
Patterns tab
nuna ornaments 2
NL-076 · volume note · volume two, census
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.
Patterns tab
nuna ornaments 2
NL-077 · law · census, alphabet, complete
Every ornament an 8-way symmetric seed within radius 6 can grow has been found, for all four 24-neighbour rules, by trying every seed rather than sampling.
96,242 seeds, each grown to rest on a 64-place board (none reached its edge, none ran past 3,000 generations). Default: 11,786 ornaments (11,052 still, 734 pulsing). Labyrinth: 24,103 (20,975 still, 3,128 pulsing). Both fail: 17,661 (17,562 still, 99 pulsing). Island: 2,460 (1,746 still, 714 pulsing). Pulsing ornaments counted once each; turns and mirrors folded. The sampled estimate of about 11,000 for Default was close; the sample had found 10,165.
default · labyrinth · both_fail · island
nuna-life-alphabets-r5-r6.json
Patterns tab · Shapes tab · type and glyph design · research
NL-048
Patterns tab
NL-078 · law · census, alphabet, correction
Enumerating all 2,119 radius-5 seeds confirms the Default and Island alphabets exactly, and finds 20 Labyrinth and 2 Both fail ornaments the sampled census missed.
Default 572 and Island 141 distinct ornaments, identical to the published sets. Labyrinth 897 (published set 877 distinct), Both fail 686 (684). The published lists also hold some pulsing ornaments twice at different phases: 10 in Default, 62 in Labyrinth, 4 in Both fail and 6 in Island, which is why their listed counts (582, 939, 688, 147) differ from the distinct counts.
default · labyrinth · both_fail · island
nuna-life-alphabets-r5-r6.json
Patterns tab
NL-076
Patterns tab
NL-079 · method · method, census
A seed space small enough to list should be listed: every seed tried once, each ornament fingerprinted by its canonical form folded over turns, mirrors and every phase of its beat. Sampling until nothing new appears can stop short, and here it did, at radius 5 under Labyrinth and Both fail.
Radius 5: 2,119 seeds in about 4 seconds per rule. Radius 6: 96,242 seeds in about 3 minutes per rule, in plain JavaScript with the nuna life engine. Radius 7 should be the next to try this way before it is declared too large.
every census
Patterns tab
NL-080 · law · census, alphabet, complete, correction
Radius 7 is not too large to finish. Every one of its 5,298,236 seeds has been grown under the Default rule, and its alphabet holds 377,560 ornaments, more than three times the estimate.
377,560 ornaments (350,382 still, 27,178 pulsing, with beats from 2 to 20); 379,791 seeds die. Run in 22 saved chunks of 250,000 seeds with no gaps; 401 ornaments spread across the alphabet regrew from their seed codes with the same beat and size; all 11,786 radius-6 ornaments reappear at radius 7, as they must. The estimate in NL-076 was about 109,000. Radius 8 has 905,607,229 seeds and remains out of reach by this method.
default
nuna-life-alphabet-r7-default.json
Patterns tab · type and glyph design · research
NL-048, NL-076
Patterns tab
What the Game of Life on the nuna lattice has taught, written to be carried into whatever comes next.
Nothing in nuna life is drawn. A seed of a few tiles goes in, and the rule decides everything after. The ornaments, cloths, gliders and fires are found, not designed, and that is where their authority comes from: each one is the only thing those tiles could have become. To make something new, change the seed or change the rule, never the result.
The rules treat every direction alike, so a symmetric seed can only grow a symmetric shape. Beauty is chosen at the seed: an 8-way seed grows an 8-way ornament, a single mirror grows a face or a letter, a turning seed grows a pinwheel.
Most growth ends. A seed under the default rule churns for a few generations or nearly a thousand, then stops, or settles into a steady beat. That resting form is the ornament: a kind of equilibrium, a negotiation the rule finished. Watching it grow is watching the negotiation.
The same seed grown under another rule is the same idea in another material:
So a rule never disqualifies a pattern; it gives it a material. If a rule rules out something interesting, change the rule, or give the changed rule its own section.
Every shape has relatives, and its family tree is part of what it is.
Pieces close enough to touch negotiate their borders:
Room is a material too: three places of it lets each piece stay itself.
Cloths can hold still, beat, or travel, and a missing tile in one heals, scars, fuses or melts. A pattern is a behaviour as much as an image, so file it with its motion, its period, and what it does when damaged.
Making something the catalogue doesn't have is the point. Anyone can find it, and it can be filed.
Every piece is a code that opens in every edition, both books, the games and the puzzle maker. What is found in one place seeds the next. The oracle is that seeding made deliberate: each discovery filed with its evidence, its rules, its examples and the projects it could carry to.
For Aaron to write
What the ornaments are to you, in your own words. Where they came from, and which ones you keep returning to.