Larger than Life

2018-03-30T00:15:08Z

Andrew: removed references to 3.0b1

{{Glossary}}
'''Larger than Life''' (abbreviated as '''LTL''' or '''LtL''') is an algorithm that supports a family of [[rule]]s with an extendable [[neighbourhood]], as defined by [[Kellie Michele Evans]] in her 1996 thesis.

==Notation==
Larger than Life rules are supported by [[Golly]] 3.0 and onwards, using the following notation, created by [[Mirek Wójtowicz]] for [[Mirek's Cellebration|MCell]]:

:<tt>Rr,Cc,Mm,Ssmin..smax,Bbmin..bmax,Nn</tt>

Here:

* <tt>Rr</tt> specifies the range (<tt>r</tt> is from 1 to 500 in Golly; 1 to 10 in [[Mirek's Cellebration|MCell]]).
* <tt>Cc</tt> specifies the number of states (<tt>c</tt> is from 0 to 255 in both Golly and MCell{{refn|group=note|The documentation for [[Mirek's Cellebration|MCell]] specifies a maximum of 25 states; this is a typo.}})
* <tt>Mm</tt> specifies if the middle cell is included in the neighborhood count (<tt>m</tt> is 0 or 1).
* <tt>Ssmin..smax</tt> specifies the count limits for a state 1 cell to survive.
* <tt>Bbmin..bmax</tt> specifies the count limits for a dead cell to become a birth.
* <tt>Nn</tt> specifies the extended neighborhood type (<tt>n</tt> is <tt>M</tt> for [[Moore neighbourhood|Moore]] or <tt>N</tt> for [[von Neumann neighbourhood|von Neumann]]).

This diagram shows the extended Moore and von Neumann neighborhoods for range 3:

{| style="margin-left: auto; margin-right: auto;"
|-
| [[File:Mooreneighbourhood range3.png]]
| [[File:Vonneumannneighbourhood range3.png]]
|}

If the number of states (specified after <tt>C</tt>) 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. <tt>C0</tt> and <tt>C1</tt> are equivalent to <tt>C2</tt>.

==Examples==
The <tt>Patterns/Larger-than-Life</tt> folder included with [[Golly]] contains a number of example patterns (mostly from the [[Mirek's Cellebration|MCell]] collection). The following table shows a number of example rules along with their commonly used names:

{| class="wikitable" style="margin-left: auto; margin-right: auto;"
|-
! Rule
! B/S equivalent
! Name
! Remarks
|-
| <tt>R1,C0,M0,S2..3,B3..3,NM</tt>
| B3/S23
| [[Conway's Game of Life|Life]]
| the default rule for this algorithm in Golly.
|-
| <tt>R5,C0,M1,S34..58,B34..45,NM</tt>
| —
| [[Bugs]]
| a chaotic rule by [[Kellie Evans]].
|-
| <tt>R10,C0,M1,S123..212,B123..170,NM</tt>
| —
| [[Bugsmovie]]
| a chaotic rule by [[David Griffeath]].
|-
| <tt>R8,C0,M0,S163..223,B74..252,NM</tt>
| —
| [[Globe]]
| an expanding rule by [[Mirek Wójtowicz]].
|-
| <tt>R1,C0,M1,S1..1,B1..1,NN</tt>
| B1/S0V
| [[Gnarl]]
| an exploding rule by [[Kellie Evans]].
|-
| <tt>R4,C0,M1,S41..81,B41..81,NM</tt>
| —
| [[Majority]]
| a stable rule by [[David Griffeath]].
|-
| <tt>R7,C0,M1,S113..225,B113..225,NM</tt>
| —
| [[Majorly]]
| an expanding rule by [[David Griffeath]].
|-
| <tt>R10,C255,M1,S2..3,B3..3,NM</tt>
| —
| [[ModernArt]]
| a chaotic rule by [[Charles A. Rockafellor]].
|-
| <tt>R7,C0,M1,S100..200,B75..170,NM</tt>
| —
| [[Waffle]]
| an expanding rule by [[Kellie Evans]].
|}

==Alternative rule notations==
Golly also allows 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:

:<tt>r,bmin,bmax,smin,smax</tt>

[[Catagolue]] uses a related notation in which the letter <tt>t</tt> ("to") is used to indicate birth/survival condition ranges:

:<tt>r</tt>''R''<tt>b</tt>''Bmin''<tt>t</tt>''Bmax''<tt>s</tt>''Smin''<tt>t</tt>''Smax''

These notations assume an extended [[Moore neighbourhood]] in which a live middle cell is included in the neighbourhood count. For example, [[Conway's Game of Life|Life]] can be entered as <tt>1,3,3,3,4</tt> in Evans' notation.

==Generalizing LtL rules to different ranges==
Larger than Life rules can be generalized ("converted") to different ranges. To convert the range-''r0'' rule <tt>Rr0,Cc,Mm,Ssmin0..smax0,Bbmin0..bmax0,Nn</tt> to a range-''r1'' rule:

# Compute ''N'' = (2 · ''r1'' + 1)2 / (2 · ''r0'' + 1)2.
# 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 <tt>Rr1,Cc,Mm,Ssmin1..smax1,Bbmin1..bmax1,Nn</tt>.

===Example===
For example, converting the range-2 rule <tt>R2,C0,M1,S5..9,B7..9,NM</tt> to range 7, 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, <tt>R7,C0,M1,S45..81,B63..81,NM</tt>.

==Also see==
* [[Generations]]

==Notes==
<references group="note" />

==References==
{{LinkMirek|filename=rullex_lgtl.html|title=Cellular Automata rules lexicon: Family: Larger than Life}}
* [[Kellie Michele Evans]]: [http://www.csun.edu/~kme52026/thesis.html Larger than Life: ''it's so nonlinear''] (1996 Ph.D. thesis)

==Further reading==
* [[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

==External links==
{{LinkForumThread|f=11|t=2933|title=Larger than Life}}

[[Category:Algorithms]]
[[Category:Cellular automata]]
[[Category:Larger than Life| ]]

Andrew Trevorrow

2009-06-26T23:21:02Z

Andrew:

{{Person|name=Andrew Trevorrow|born=1955|alma=R.M.I.T.|inst=n/a|res=Melbourne|nat=Australian}}
'''Andrew Trevorrow''' is a [[Conway's Game of Life|Life]] enthusiast and computer programmer who has coded many important Life programs and discovered some interesting patterns. His most notable Life program is [[Golly]], which he coded with [[Tomas Rokicki]]. A few years earlier he coded [[LifeLab]], a Macintosh-only Life simulator.

The most notable pattern that he discovered is [[bunnies]] (and the related [[rabbits]]), and he has studied the [[Long Life]] rule.

{{PatternsFoundBy|name=Andrew Trevorrow}}

==References==
*{{cite web|url=http://entropymine.com/jason/life/status.html |title=Game of Life Status page |accessdate=April 20, 2009}}
*{{cite web|url=http://home.interserv.com/~mniemiec/lifecred.htm#elkies |publisher=Mark D. Niemiec |title=Life Credits |accessdate=May 8, 2009}}

==External links==
*[http://www.trevorrow.com/ Homepage] of Andrew Trevorrow

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2009-06-02T06:05:23Z

Andrew:

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Larger than Life

Andrew Trevorrow

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