Larger than Life
|It has been suggested that this article or section be merged into Totalistic Life-like cellular automaton. (Discuss)|
- Rr specifies the range (r is from 1 to 500 in Golly and LifeViewer; 1 to 10 in MCell).
- Cc specifies the number of states (c is from 0 to 255 in Golly, LifeViewer and MCell[note 1])
- Mm specifies if the middle cell is included in the neighborhood count (m is 0 or 1).
- Ssmin..smax specifies the count limits for a state 1 cell to survive.
- Bbmin..bmax specifies the count limits for a dead cell to become a birth.
- Nn specifies the extended neighborhood type (n is M for Moore or N for von Neumann. Golly and LifeViewer also support C for Circular neighborhood. LifeViewer additionally supports 2 for L2, + for Cross, X for Saltire and * for Star neighborhoods and many more).
This diagram shows the extended Moore and von Neumann neighborhoods for range 3:
If the number of states (specified after C) is greater than 2, then states 1 and above don't die immediately but gradually decay. Note that state values above 1 are not included in the neighborhood counts and thus play no part in deciding the survival of a state 1 cell, nor the birth of an empty cell. C0 and C1 are equivalent to C2.
The Patterns/Larger-than-Life folder included with Golly contains a number of example patterns (mostly from the MCell collection). The following table shows a number of example rules along with their commonly used names:
|R1,C0,M0,S2..3,B3..3,NM||B3/S23||Life||the default rule for this algorithm in Golly.|
|R5,C0,M1,S34..58,B34..45,NM||—||Bugs||a chaotic rule by Kellie Evans.|
|R10,C0,M1,S123..212,B123..170,NM||—||Bugsmovie||a chaotic rule by David Griffeath.|
|R8,C0,M0,S163..223,B74..252,NM||—||Globe||an expanding rule by Mirek Wójtowicz.|
|R1,C0,M1,S1..1,B1..1,NN||B1/S0V||Gnarl||an exploding rule by Kellie Evans.|
|R4,C0,M1,S41..81,B41..81,NM||—||Majority||a stable rule by David Griffeath.|
|R7,C0,M1,S113..225,B113..225,NM||—||Majorly||an expanding rule by David Griffeath.|
|R10,C255,M1,S2..3,B3..3,NM||—||ModernArt||a chaotic rule by Charles A. Rockafellor.|
|R7,C0,M1,S100..200,B75..170,NM||—||Waffle||an expanding rule by Kellie Evans.|
Notable patterns which are frequently found within Larger than Life rules include "bugs", which are patterns (usually spaceships, but sometimes oscillators) which are hollow, characterised by those from Bosco's Rule, "solid ships", which are typically extremely slow circular spaceships first noted in 2002 (such as this one), and "roomba bugs", travelling patterns that usually stabilise into low-period oscillators after intense amounts of generations but are infrequently found to be real spaceships.
Alternative rule notations
Golly and LifeViewer also allow rules to be entered using the notation defined by Kellie Evans in her thesis. The range, birth limits and survival limits are specified by five integers separated by commas:
Catagolue, apgsearch and LifeViewer use a related notation in which the letter t ("to") is used to indicate birth/survival condition ranges; the initial gC is optional, with the number of states defaulting to two:
Generalizing LtL rules to different amounts of neighbors
Larger than Life rules can be generalized ("converted") to different ranges and even neighborhoods. To convert the range-r0 n0-neighborhood rule Rr0,Cc,Mm,Ssmin0..smax0,Bbmin0..bmax0,Nn0 to a range-r1 n1-neighborhood rule:
- Compute N to equal the ratio of the number of neighbors in a range-r1 n1-neighborhood to the number of neighbors in a range-r0 n0 neighborhood.
- Multiply the original rule's minimum and maximum birth/survival conditions by N and round off, to wit:
- Compute smin1 = round(smin0 · N).
- Compute smax1 = round(smax0 · N).
- Compute bmin1 = round(bmin0 · N).
- Compute bmax1 = round(bmax0 · N).
The converted rule is Rr1,Cc,Mm,Ssmin1..smax1,Bbmin1..bmax1,Nn1.
For example, converting the range-2 rule R2,C0,M1,S5..9,B7..9,NM to range 7 with the same neighborhood, with the formula for the number of neighbors in a range-r Moore neighborhood being (2 · r + 1)2, we obtain:
- N = (2 · 7 + 1)2 / (2 · 2 + 1)2 = 225 / 25 = 9.
- smin1 = 5 · 9 = 45.
- smax1 = 9 · 9 = 81.
- bmin1 = 7 · 9 = 63.
- bmax1 = 9 · 9 = 81.
The converted rule is, therefore, R7,C0,M1,S45..81,B63..81,NM.
- The documentation for MCell specifies a maximum of 25 states; this is a typo.
- Cellular Automata rules lexicon: Family: Larger than Life at Mirek Wójtowicz's Cellebration page
- Kellie Michele Evans: Larger than Life: it's so nonlinear (1996 Ph.D. thesis)
- Kellie Michele Evans: Larger than Life's Extremes: Rigorous Results for Simplified Rules and Speculation on the Phase Boundaries, in: Andrew Adamatzky (ed.), Game of Life Cellular Automata, Springer (London) (2010), ISBN 978-1-84996-216-2, OCLC 619946115
- Kellie Michele Evans: Larger than Life, in: Andrew Adamatzky, Genaro J. Martínez (eds.): Designing Beauty: The Art of Cellular Automata, Springer (2016), ISBN 978-3-319-27269-6, OCLC 934720008
- Larger than Life (discussion thread) at the ConwayLife.com forums