Planar Trivalent Network Computation
Planar Trivalent Network Computation
复制标题
平面三价网络计算
DOI：
10.1007/978-3-540-74593-8_13
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
T. Bolognesi
中科院分区：
文献类型：
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作者：
T. Bolognesi
S.Wolfram研究了巨型三价网络的汇流重写系统，作为空间和时空的可能模型，以雄心勃勃地寻找最基本的物理计算定律。我们在这里仅限于平面三价网，它们被证明支持图灵完全计算，并采取了更激进的方法：当操作网络对偶时，我们只使用一个初等重写规则，并通过简单的、完全确定的算法而不是模式匹配来驱动其应用。我们设计了有效的可视化指示器来探索具有基本初始条件的计算的复杂性，包括数千个图，并揭示了从规则到随机的丰富多样的行为。在它们的特征中，我们特别研究了涌现空间的维度。
Confluent rewrite systems for giant trivalent networks have been investigated by S. Wolfram as possible models of space and spacetime, in the ambitious search for the most fundamental, computational laws of physics. We restrict here to planar trivalent nets, which are shown to support Turing-complete computations, and take an even more radical, approach: while operating on network duals, we use justoneelementary rewrite rule and drive its application by a simple, fully deterministic algorithm, rather than by pattern-matching. We devise effective visual indicators for exploring the complexity of computations with elementary initial conditions, consisting of thousands of graphs, and expose a rich variety of behaviors, from regular to random-like. Among their features we study, in particular, the dimensionality of the emergent space.