Editing Life-like cellular automaton (section)

==Generalizations==
There are other cellular automata which are inspired by the Game of Life, but which do not fit the definition of
"{{Not a typo|life-like}}" given in this article, because their neighborhoods are larger than the Moore neighborhood, or
they are defined on three-dimensional lattices, or they use a different lattice topology.  For example:

*''[[Non-totalistic]] rules'' depend on the configuration of live cells in the neighborhood.
**''Non-[[isotropic]] rules'' that behave differently in different directions. There are 2<sup>512</sup>≈1.34*10<sup>154</sup> rules of this kind, including isotropic rules.{{Citation needed|date=August 2023}}
**''Isotropic non-totalistic rules'' behave identically under rotation and reflection. There are 2<sup>102</sup>≈5.07*10<sup>30</sup> rules of this kind, including outer-totalistic rules.<ref>{{citation
 | last = Sapin | first = Emmanuel
 | editor-last = Adamatzky | editor-first = Andrew | editor-link = Andrew Adamatzky
 | doi = 10.1007/978-1-84996-217-9_9
 | issue =
 | title = Game of Life Cellular Automata
 | pages =135–165
 | contribution = Larger than Life: threshold-range scaling of Life's coherent structures
 | volume =
 | year = 2010}}</ref>
*''Generations'' rules include one or more "dying" states cells switch to instead of instantly dying. The most famous examples in this category are the rules "Brian's Brain" (B2/S/3) and "Star Wars" (B2/S345/4). Random patterns in these two rules feature a large variety of spaceships and rakes with a speed of c, often crashing and combining into even more objects.
*''Larger than Life'' is a family of cellular automata studied by Kellie Michele Evans.  They have very large radius neighborhoods, but perform "birth/death" thresholding similar to Conway's life.  These automata have eerily organic "glider" and "blinker" structures.<ref>{{citation
 | last = Evans | first = Kellie Michele
 | doi = 10.1016/S0167-2789(03)00155-6
 | issue = 1–2
 | journal = Physica D
 | pages = 45–67
 | title = Larger than Life: threshold-range scaling of Life's coherent structures
 | volume = 183
 | year = 2003| bibcode = 2003PhyD..183...45E
 }}.</ref>
*''RealLife'' is the [[continuum limit]] of Evan's Larger Than Life CA, in the limit as the neighborhood radius goes to infinity, while the lattice spacing goes to zero.  Technically, they are not cellular automata at all, because the underlying "space" is the continuous Euclidean plane '''R'''<sup>2</sup>, not the discrete lattice '''Z'''<sup>2</sup>.  They have been studied by Marcus Pivato.<ref>{{citation
 | last = Pivato | first = Marcus
 | arxiv = math.DS/0503504
 | doi = 10.1016/j.tcs.2006.11.019
 | issue = 1
 | journal = Theoretical Computer Science
 | pages = 46–68
 | title = RealLife: the continuum limit of Larger than Life cellular automata
 | volume = 372
 | year = 2007}}.</ref>
*''[[Lenia]]'' is a family of continuous cellular automata created by Bert Wang-Chak Chan. The space, time and states of the Game of Life are generalized to continuous domains, using large neighborhoods, fractional updates, and real number states, respectively.
*Carter Bays has proposed a variety of generalizations of the Game of Life to three-dimensional CA defined on '''Z'''<sup>3</sup> ([[3D Life]]).<ref>{{citation
 | last = Bays | first = Carter
 | issue = 4
 | journal = Complex Systems
 | pages = 381–386
 | title = A note about the discovery of many new rules for the game of three-dimensional life
 | volume = 16
 | year = 2006}}.</ref>  Bays has also studied two-dimensional {{Not a typo|life-like}} CA with triangular or hexagonal neighborhoods.<ref>{{citation
 | last = Bays | first = Carter
 | issue = 4
 | journal = Journal of Cellular Automata
 | pages = 345–350
 | title = The discovery of glider guns in a game of life for the triangular tessellation
 | volume = 2
 | year = 2007}}.</ref><ref>{{citation
 | last = Bays | first = Carter
 | issue = 3
 | journal = Complex Systems
 | pages = 245–252
 | title = A note on the game of life in hexagonal and pentagonal tessellations
 | volume = 15
 | year = 2005}}.</ref>