RealLife: The continuum limit of Larger than Life cellular automata
RealLife: The continuum limit of Larger than Life cellular automata
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现实生活：大于生命元胞自动机的连续极限
DOI：
10.1016/j.tcs.2006.11.019
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
M. Pivato
中科院分区：
文献类型：
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作者：
M. Pivato
设A≔{0,1}。元胞自动机（CA）是由局部规则确定的[公式：见文本]的轮班通勤变换。同样，欧几里得自动机（EA）是由局部规则确定的[公式：参见文本]的换班变换。大于生命 (LtL) CA 是 J.H.康威的生命游戏 CA，由 K.M. 提出埃文斯。我们证明了 Evans 的一个猜想：当它们的半径增长到无穷大时，LtL CA 收敛到一个“连续极限”EA，我们称之为 RealLife。我们还表明，LtL CA 的生命形式（不动点、周期轨道和传播结构）收敛于 RealLife 的生命形式。最后我们证明了现实生活中不动点的多个存在性结果。
Let A≔{0,1}. A cellular automaton (CA) is a shift-commuting transformation of [Formula: see text] determined by a local rule. Likewise, a Euclidean automaton (EA) is a shift-commuting transformation of [Formula: see text] determined by a local rule. Larger than Life (LtL) CA are long-range generalizations of J.H. Conway’s Game of Life CA, proposed by K.M. Evans. We prove a conjecture of Evans: as their radius grows to infinity, LtL CA converge to a ‘continuum limit’ EA, which we call RealLife. We also show that the life forms (fixed points, periodic orbits, and propagating structures) of LtL CA converge to life forms of RealLife. Finally we prove a number of existence results for fixed points of RealLife.