Tony Smith's small corner of WMPVN rule space

Smith's invention of the WMPVN rule space came as he wrapped up two years of data collection relating to Generations 345/3/6 aka LivingOnTheEdge (LOTE), and was prompted by a lack of close comparators for the emergent phenomena which had kept him so interested in LOTE. (Writing up those LOTE results will take a lot more time to achieve an adequate representation.)

Rather than try random exploration of the much larger WMPVN rule space, Smith chose to focus the next phase of his cellular automata project on a comfort zone within the WMPVN space which could be shown analytically to potentially support some of the base level emergent phenomena which appeared to be particularly important to the ultimate emergence of the diversity of higher level phenomena that emerge in LOTE.




Count range









1/2 forward movement

born 3

born 45

1/2 toggling side cells

born 3

born 4

asym ship central cell death

not survive 6

not survive 9

sym ship central cell death

not survive 7

not survive a

tail/edge clean up

not survive 12

not survive (1?)23

track without gap stability

survive 35

survive 48

double track with gap stability

survive 34

survive 46

gapless double track stability

survive 345

survive 468

block stability

survive 3

survive 5

blocked track stability

survive 5

survive 8

gap stability

not born 4

not born 6(7?8?)

track toothed edge stability

not born 5

not born 8

Smith's primary method of study is to identify rules which support relatively slow total pattern growth from the tiny fraction of simple seed patterns that prove viable in such rules and then to run those patterns for of order 100,000 iterations. Discussion of the more recognisable emergent phenomena unavoidably invokes terminology which he has added over the years to the basic cellular automata vocabulary that has been recorded in Stephen Silver's Life Lexicon. A specialised glossary for LOTE is in preparation, although many of the sometimes self-explanatory images and animations it will use are online already.

Headline discoveries

WMPVN-45678c_459abc_12 forms a small seed pattern which replicates itself in 163 iterations rotated 90° 46 cells apart diagonally, cumulatively emulating Ed Fredkin's XOR-based replicator, at least on the sometimes permeable diamond-shaped skin which forms around what would otherwise be a slower-growing growing core.

(As shown in the background to this page) WMPVN-45678x_459_17 forms an active shoulder which stretches the 4 in 6 sloping leading edge of a pattern 4 cells wider every 152 iterations behind whatever puffer engine initiated the original growth. "Braids" with a 3 cell wide chequerboard core and "gutters" form trailing the leading edge, some eroding away but others lengthening to leave a pattern of mostly active gaps which eventually stabilise distinctively for the two variant rules (survive c or not). The growth shoulder sometimes regenerates after disturbance while a range of constrained environments form inside the ever-growing overall pattern.

WMPVN-45678c_459ac_16 is one of the large block of rules (WMPVN-45678x_459axx_11&16+) dominated by a ubiquitous pattern which reforms 14 cells away in 39 iterations as a ship, puffer, delta or space filler. In general those which are space fillers or self producers form settled cores but in this one rule the core stays active, albeit with chaotic core expanding a lot more slowly within the 56x56 repetitive patterns in growing triangles which come to dominate each quadrant. The most common reprocessing delta advances 168 cells (3 repeats) every 700 iterations. These have even been seen in comb formations amongst a diversity of other boundary processes. (Early work with eroding agars in Life initiated anticipation that such a rule might exist.)

While all rules in the comfort zone produce common (space)ships which advance 1 cell per 2 iterations and form widening outbound streams from the growing core of each viable pattern, in the WMPVN-45678bx_459xxx_16+ quarter of the WMPVN zone a ubiquitous "flutterby" moves 13 cells diagonally every 58 iterations creating a ship stream background in the shape of an 8 point compass. When a "delta" (widening puffer trail with lateral rakes) forms under such rules, repeated interactions between rake ships and forward and backward flutterby rakes form large scale patterns.

Amongst the unending emergence of novel mechanisms, cellular automata traditions make the WMPVN-45678_45xbx_7+ knight ship and WMPVN-45678bx_459axx_11+ knight trail noteworthy.