Wild emergence
of complex organisation
in a simple cellular automata
Tony Smith
Meme Media
Wild emergence ...
Six months intense study of the development from simple seeds with the Generations 345/3/6 cellular automata rule has revealed a vast new territory of emergent phenomena and a limitless supply of data on the behaviour of complex interactions extremely close to the elusive boundary of order and chaos. Viable seed patterns form a slowly growing chaotic core with outbound streams of 1/2 speed (space)ships headed NSEW. Around once per million live cells, one of several varieties of also 1/2 speed track/trail laying engines appears, surviving indefinitely within the ship streams. The tracks and trails exhibit resilience, even healing, and support a range of attached patterns moving at various fractional speeds. Those attached patterns and subsequent interactions with ships in the streams provide numerous different mechanisms for initiating new chaotic cores far from the original core. Most important reactions exhibit phase dependent variability making them computationally irreducible and attractive for statistical analysis despite being fully deterministic.
Generations 345/3/6 ‘LivingOnTheEdge’
- Some background
- A journey of discovery
- Categories of emergent phenomena
- The communication challenge
Cellular Automata
- John Horton Conway’s Game of Life (1970)
- Fredkin’s (1983) inspires Pattern Breeder☯
- FullPaint Easter egg reveals Life in a Tube☯ and eroding agars☯
- Stephen Wolfram’s four classes (1983) and A New Kind of Science (2002)
- Trapper☯ (1-D found in narrow Tubes)
Constraining Life in quest of the Edge*
*Border of Order–Edge of Chaos
- On left, Life in a Tube produces minimalist ‘metabolic’ pathways.
- At right, a 4/5 speed eroding leader forms copies of itself at 90°. (Image links to 4Mb animation.)
Andrew Trevorrow
- LifeLab for Macintosh, Join Edges, Tile …
- RLE to animated GIF in Perl
- Andrew goes Open Source with his successor CA project
- Golly designed for heavy GoL engineering
- Version 2.0 adds many new rule classes
http://golly.sf.net/
At this point of the presentation, switch to Golly running the ticker then Open Recent ortho-60000, zoom in and scroll around before resuming slides.
Generations 345/3/6 ‘LivingOnTheEdge’
- Live cells with 3, 4 or 5 neighbours live
- Dead cells with 3 neighbours come alive
- 6 = live+dead+4 dying states/iterations out
- Found and named in February 2000 by MCell/MJCell author Mirek Wojtowicz who noted: “In this very chaotic rule it’s hard to tell if patterns will survive or die out.”
[any material that should appear in print but not on the slide]
My test seed: ‘The Wild’*
* a fortuitous mistake!
Plenty to keep watching: iteration 9661
Click through to animation of iterations 9000-10000.
The first “engine”
Early “Alpha” shown here in Golly’s default colour scheme.
Track-laying Alpha forms after iteration 55,700, laying an often-eroding track before converting to a puffer engine around 114,300, the first puff from which eventually reactivates to seed soon rapidly growing “Honalee”.
Phase dependent reblocking/conversion
Realigned for comparison of alternate erosion phases, The Wild’s 3rd (top) and Alpha engines.
Ship flow dynamics
- Ships and engines run 1 cell per 2 iterations
- Ship/track/trail interactions in cross and head-on flows produce range of outcomes
- Puffer rakes clear a cross-flow alignment
- Ships run into anchor blocks at the back of tracks which then erode at 6 cells per 10 iterations until reblocking at the engine
Homer's conversion
A second engine “Homer” forms after iteration 125,000, initially laying a block trail before converting to track laying.
Stories great and small
- Each new engine-plus-trail is a unique story
- Honalee grows rapidly against the flow as ship interactions seed new active spots
- Tracks, block and puffer trails across and against ship flow fare very differently
- “Wreckage” of ships into tracks 50:50
- “Shifters” traverse block trails at 2/5 speed
Unbelievably cute “Hanu”
Then, on Homer’s track, the discovery which went as close as anything could to having me question my lack of faith.
Painting the big picture
- Patterns grow NSEW at ship/engine speed
- Default compression looses much detail so use custom colours for 48x48 cells:1 pixel
- Details need animation with pan and zoom
- Extensive descriptive notes/commentary
- Systematic study of common interactions
- Harder to study chaotic core processes
“Whoa”
- Of possible head on collisions between 2 common ships, 3 sustain limitless growth:
- ubiquitous “ddsym”
- a 180° rotationally symmetric seed
- asymmetric Whoa.
- Bill Hall had long asked what happens when we break the seed symmetry (and still wants to call it “Big Bang in Flatland”).
- Whoa’s answer was “four times as much” per computer cycle.
Surprises keep coming
- A new iMac ran The Wild on from 222,000 to 225,000 before switching to run Whoa on from 200,000 and it is still running 24/7, saving snapshots every 200 iterations.
- The old iMac is running common collision products to 100,000 and some beyond.
- Six months on, something unanticipated emerges almost every other day.
Four trail/engine classes
- Track laying. Some short engines have a 50:50 chance of converting when track erosion reaches the engine.
- Puffer. P.192. En passant reaction variant.
- Block trail. Off-centre and p.32 variants.
- Delta. P.56 doubling. Two versions with a subtle switch making a major difference.
Ecosystem:Track:Wreckage
Ecosystem:Track:Tagalongs
Ecosystem:Trail:Shifters
Always damaging lateral interactions with trails are phase dependent with shifters making phase changes, though normally a lot less often than in the constructed demonstration here. Gobblers consume undamaged trails at 8/13 until they are blocked by shifter or engine.
Characteristics of viable seeds
- Cell count exceeds iteration count beyond iteration 1000
- Core starts out irregular
- Growth through bursts
- Tends roughly circular
- Growth through infill
- Tends roughly square
- Growth through engines spreading remote seeds
- Wild diversification
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Growth curves follow a familiar theme
Spreading the chaos
- Remote puffer conversion: Honalee
- Tagalong overload (and shiftalongs)
- Track deblocking debris
- Skimming ship into shifter
- Gobbler into shifter or engine
- Naked Delta (and deltoid puffer)
- Erosion producing non 1/2 speed rake
- Rugby
- Diagonal and double mid line symmetries
Strategic opportunities
- Limitless supply of data on undisturbed emergence from trivial seeds under a fully deterministic and repeatable process.
- Educational demonstration of an emergent theoretical framework for NN Taleb’s Black Swans and Rumsfeld’s unknown unknowns.
- Restore focus to border of order–edge of chaos and to computational irreducibility.
- Engineering possibilities (never my focus).
Data points
- Attractor basins for engine form creation, conversion and deltoid period doubling.
- Population growth variability.
- Interaction combinatorics, e.g. 18 outcomes in period 42 cycle of Gobbler into shifter.
- Survival times of engines, tracks.
- “Shell collecting” amongst the chaos.
Nurturing systemic thinking
- Salner 1986 identifies the problem
- Making this story accessible
- Counterpoint to “intelligent design”
- Appropriate media and forums
- Drawing practical lessons
- Leaving traces
- Growth imperative
- First mover advantage
- Thinking skills for issues of our time
Border of order–edge of chaos
- Langton’s λ—an oversimplification
- Dampening effect of Mitchell, Hraber and Crutchfield’s failure to disprove null hypothesis
- Wolfram’s Class 4 (1983) and Principal of Computational Equivalence (2002)
- Generations rule space tuning mechanism?
Engineering possibilities
- Chaos keeps growing
- Maze-like areas, their holes and boundaries can be locally stable
- Single live cell running around blocks creates oscillator periods ≥ 6
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Natural example of signal induction found near new engine
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Where to from here?
- http://www.TheWildCA.com/
- Imagining Pythagorus
- Naturally occurring statistical sampler with data recording, readout and, after late stage phase change, a gun.
- 15th IFIP workshop on Cellular Automata and Discrete Complex Systems, October 10-12, Brazil. May 24 submission deadline.
- 4th Australian Conference on Artificial Life, December 1-4, Melbourne. June 16 deadline.
- Feature length fully generated HD video?
- Aesthetics, programming, processing power
Comments? Questions!
Thank you
