Universal dynamical computation in multidimensional excitable lattices
Universal dynamical computation in multidimensional excitable lattices
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DOI：
10.1023/a:1026604401265
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发表时间：
1998-12-01
影响因子：
1.4
通讯作者：
Adamatzky, A
中科院分区：
文献类型：
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作者：
Adamatzky, A
我们研究二维和三维晶格节点采取三种状态：休息，兴奋。和不应性，并根据激发的最近邻的数量在离散时间内确定性地更新它们的状态。每个静止节点被激发，如果它的8个（在二维晶格中）或它的26个（在三维晶格中）最接近的邻居中的正好2个被激发。节点无条件地将其兴奋状态改变为不应状态，并且将其不应状态改变为休息状态。我们证明，这样的晶格是晶格激发的最小模型，表现出有界可移动的自局域激发模式（粒子状波）。最小的，紧凑的。稳定的、不可分割的、能够不停地运动的粒子状波代表着信息的量子。探索所有可能的二进制粒子之间的碰撞波，我们构建的目录中实现的可激发晶格的逻辑门。逻辑运算的空间和时间复杂度进行了评估，并讨论了寄存器，计数器和反射器的可能实现。可激发晶格在计算通用模型层次结构中的位置及其与现实生活中类似物的高度亲和力证实了可激发晶格可能是类真实动态通用计算的最小模型。
We study two- and three-dimensional lattices nodes of which take three states: rest, excited. and refractory, and deterministically update their states in discrete time depending on the number of excited closest neighbors. Every resting node is excited if exactly 2 of its 8 (in two-dimensional lattice) or exactly 4 of its 26 (in three-dimensional lattice) closest neighbors are excited. A node changes its excited state into the refractory state and its refractory state into the rest state unconditionally. We prove that such lattices are the minimal models of lattice excitation that exhibit bounded movable patterns of self-localized excitation (particle-like waves). The minimal, compact. stable, indivisible, and capable of nonstop movement particle-like waves represent quanta of information. Exploring all possible binary collisions between particle-like waves, we construct the catalogue of the logical gates that are realized in the excitable lattices. The space and time complexity of the logical operations is evaluated and the possible realizations of the registers, counters, and reflectors are discussed. The place of the excitable lattices in the hierarchy of computation universal models and their high affinity to real-life analogues affirm that excitable lattices may be the minimal models of real-like dynamical universal computation.