囊泡计算机：在Voronoi自动机上逼近沃罗诺伊图
Vesicle computers: Approximating Voronoi diagram on Voronoi automata
摘要：
用限定在平面沃罗诺伊图上的有限状态机--沃罗诺伊自动机来模拟充满可激发和沉淀化学体系的囊泡的不规则排列。每个Voronoi细胞都有四种状态：静息、兴奋、不应和沉淀。如果一个静止的细胞至少有一个兴奋的邻居，那么它就会兴奋;如果在它的邻居中兴奋的细胞与它的邻居数量的比率超过一定的阈值，那么细胞就会沉淀。为了在Voronoi自动机上近似一个沃罗诺伊图，我们将一个平面集合投影到自动机格上，从而激发出对应于数据点的单元。激发波通过Voronoi自动机传播，相互作用形成沉淀。沉淀物的构型代表近似的沃罗诺伊图的边缘。发现了沃罗诺伊图逼近质量与降水阈值之间的关系，证明了该模型在任意形状物体和平面骨架的沃罗诺伊图逼近中的可行性。
英文摘要：
Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neighbourhood to its number of neighbours exceed certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate in result of the interaction. Configuration of precipitate represents edges of approximated Voronoi diagram. We discover relation between quality of Voronoi diagram approximation and precipitation threshold, and demonstrate feasibility of our model in approximation Voronoi diagram of arbitrary-shaped objects and a skeleton of a planar shape.
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