Larger than Life
Larger than Life widens Life’s neighbourhood. Instead of the eight cells around it, a cell looks
at every cell within some range r, and is born or survives when the number of live cells there
falls in a range of values. With a large enough neighbourhood, Life’s small, jagged creatures give
way to big, smooth, almost organic ones.
R5,C2,S33-57,B34-45), 300 generations after a random start on a
wrapped 200 × 125 grid. Each cell counts the live cells in the 11 × 11 box around it. Watch the soup
die back within a few generations, leaving hollow blobs that wobble, merge and break up; the small
ones that keep their shape and travel are the "bugs" the rule is known for. Scene
docs/scenes/automata/ltl-bosco.json.What it is
A Larger than Life rule has a range r, a neighbourhood shape, and a birth and
survival condition given as ranges of counts:
- On the square grid, the usual (Moore) shape is the box of side
2r + 1around the cell, so a range-5 cell has 120 neighbours. The von Neumann shape is the diamond of cells withinrsteps up, down, left and right. - A dead cell is born when the number of live cells in its neighbourhood is in the birth range; a live cell survives when the count is in the survival range.
Life is the range-1 case. Larger ranges average over more cells, which smooths out the randomness of small counts: patterns grow round edges and move as large coherent bodies. Kellie Evans showed that rescaled versions of Life’s gliders and replicators exist at large ranges; Evans called the gliders “bugs” (Evans 1996).
The modern generalisation, higher-range outer-totalistic (HROT) rules, allows any list of counts rather than a single interval for birth and for survival (LifeWiki: HROT).
Where it came from
Golly’s documentation credits David Griffeath with first imagining Larger than Life in the early 1990s, to see whether Life sits near a critical point when its thresholds and range are scaled up together (Golly: Larger than Life). Golly cites Griffeath’s “Self-organization of random cellular automata: four snapshots” as the first reference (Griffeath 1994).
Kellie Michele Evans developed the family in a 1996 PhD thesis at the University of Wisconsin–Madison, Larger than Life: It’s So Nonlinear, supervised by Griffeath. Evans’s preface says the question came from Griffeath: would glider-like “digital creatures” emerge from random starts if Life’s rule were rescaled to larger neighbourhoods? The thesis studies the family with tools from probability and from dynamics, including large-range analogues of Life’s replicators and gliders (Evans 1996). Evans continued the work in a series of papers (Evans 2001; Evans 2003; Evans 2003, replicators; Evans 2005; Evans 2010; Evans 2016).
MCell’s rules lexicon says the “Bugs” rule was found while exploring the parameter space on the CAM-8 cellular automaton machine, and credits it to Evans (MCell rules lexicon). Golly’s help says that “Bosco”, a period-166 oscillator, was discovered by Evans, and that Dean Hickerson used MCell to build the first bug gun from it (Golly: Larger than Life). The rule became known as Bosco’s Rule (LifeWiki: Larger than Life). Other named rules include Griffeath’s Majority, Majorly and Bugsmovie, Evans’s Waffle, Wójtowicz’s Globe and Charles A. Rockafellor’s ModernArt (see the catalogue).
Mirek Wójtowicz’s MCell (from 1999) gave the family its first widely used notation, with ranges up to 10 (MCell families). Chris Rowett’s LifeViewer added Larger than Life and HROT rules in January 2019, accepting Adam P. Goucher’s lifelib notation for HROT (Rowett 2019). Golly added a Larger than Life algorithm in version 3.0 (2017) and HROT rules in 4.0 (2020) (Golly changes).
How JETCARP runs it
Notation
JETCARP reads both the HROT form and MCell’s form:
| Notation | Meaning |
|---|---|
R5,C2,S33-57,B34-45 | Bosco’s Rule in HROT form: range 5, two states, survival on 33 to 57, birth on 34 to 45 |
R5,C0,M1,S34..58,B34..45,NM | The same rule in MCell’s form, where M1 counts the cell itself, so the survival bounds are one higher |
R2,C2,S4-8,B5-7,NN | The von Neumann (diamond) shape |
R3,C2,S2,B3,N+ | Factorio, on the cross-shaped neighbourhood (square grid only) |
R10,C255,S1-2,B3 | ModernArt: with more than two states, dying cells decay as in Generations |
In HROT form the centre cell is never counted. Counts can be lists of values and ranges separated
by commas. Rules with weighted or custom neighbourhoods (an NW… suffix) are not supported yet,
so the named rule Coexistence cannot be run.
On any tiling
On the square grid the Moore shape is the box and the von Neumann shape the diamond. On any other
tiling JETCARP measures range in steps over the neighbour graph: Moore means “within r steps over
touch neighbours” and von Neumann means “within r steps over edge neighbours”. On the square grid
these definitions give exactly the box and the diamond, and range 1 is checked to equal Life. The
cross shape has no such reading and stays on the square grid.
Neighbourhood sizes change with the tiling, so a rule’s thresholds usually need adjusting when it moves. On the hat, below, Bosco’s thresholds are scaled down by a quarter, and bug-like hollow blobs appear on an aperiodic tiling.
R5,C2,S25-43,B26-34): the neighbourhood is every
tile within five steps of the touch neighbour graph. The middle of a patch of about 4,000 hats, 300
generations from a random start; watch the soup clump into blobs whose edges shift and smooth
themselves over the irregular tiles. Scene docs/scenes/automata/ltl-hat.json.What is new here
Larger than Life-style range rules have run on the hat before, in Andrew Trevorrow’s HatLife (Trevorrow 2023); we did not confirm whether HatLife measures range in graph steps. Golly supports hexagonal, triangular and other neighbourhood shapes (Golly: Larger than Life). We do not claim anything new for this family. Defining range as graph distance is what lets JETCARP run the family on every tiling, including the k-uniform, isohedral and aperiodic ones.
Try it
- Quick Start: the eight runnable named rules, for example Bosco’s Rule, Majority (LtL) and ModernArt.
jetcarp run docs/scenes/automata/ltl-bosco.json --gens 300 --png bosco.png- Move Bosco’s Rule to hexagons and lower its thresholds until bugs appear; the neighbourhood of range 5 is smaller there than on squares.