论文标题
通过概率的蜂窝自动机规则形成点模式
Forming Point Patterns by a Probabilistic Cellular Automata Rule
论文作者
论文摘要
目的是找到一个蜂窝自动机规则，该规则可以形成具有最大点数（1个细胞）数量的2D点模式。点不允许彼此触摸，必须通过0个细胞将它们分开，并且每个0细胞都能在其摩尔邻居中找到至少一个点。设计了概率规则，可以通过异步更新和循环边界条件来解决此任务。该任务被认为是一个平铺问题，其中使用点瓷砖用重叠来覆盖空间。一个点瓷砖由中心像素（值1的内核）和8个以值0形成船体的像素周围的像素。该术语像素用于区分瓷砖的细胞与细胞自动机细胞的细胞。对于9个瓷砖像素中的每一个，所谓的模板都是由点瓷砖的偏移定义的。在规则应用中，在实际的单元位置测试了9个模板。如果模板的所有模板像素（除中央参考像素除外）与所考虑的实际单元格的相应邻居匹配，则将单元格的状态调整为参考像素的值。否则，该单元格设置为随机值0或1，具有一定概率。允许船体像素重叠。为了进化最大点，必须最大化瓷砖之间的重叠。为此，计数模板命中的数量。根据命中率的不同，将额外的噪声注入某些概率。因此，可以进化具有最大点数的最佳模式。为不同的参数设置评估了设计规则的行为和性能。
The objective is to find a Cellular Automata rule that can form a 2D point pattern with a maximum number of points (1-cells). Points are not allowed to touch each other, they have to be separated by 0-cells, and every 0-cell can find at least one point in its Moore-neighborhood. Probabilistic rules are designed that can solve this task with asynchronous updating and cyclic boundary condition. The task is considered as a tiling problem, where point tiles are used to cover the space with overlaps. A point tile consists of a center pixel (the kernel with value 1) and 8 surrounding pixels forming the hull with value 0. The term pixel is used to distinguish the cells of a tile from the cells of a cellular automaton. For each of the 9 tile pixels a so-called template is defined by a shift of the point tile. In the rule application, the 9 templates are tested at the actual cell position. If all template pixels (except the central reference pixel) of a template match with the corresponding neighbors of the actual cell under consideration, the cell's state is adjusted to the reference pixel's value. Otherwise the cell is set to the random value 0 or 1 with a certain probability. The hull pixels are allowed to overlap. In order to evolve a maximum of points, the overlap between tiles has to be maximized. To do that, the number of template hits is counted. Depending on the hit-number, additional noise is injected with certain probabilities. Thereby optimal patterns with the maximum number of points can be evolved. The behavior and performance of the designed rules is evaluated for different parameter settings.
