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таблице~\ref{tbl:patters} в результате анализа удалось обнаружить несколько циклических паттернов, рассмотрим их подробнее. + + \newpage + При задании начальной конфигурации <<Горизонтальная палочка>> (см. Рис.~\ref{fig:start_hline}) и нулевых или тороидальных граничных условий палочка каждый такт времени сдвигается вверх по сетке автомата на одну строку. При нулевых граничных условиях палочка доходит до границы поля и исчезает (см. Рис~\ref{fig:hline_zeros}). При тороидальных граничных условиях палочка доходит до границы, затем появляется снизу и снова движется вверх по сетке (см. Рис~\ref{fig:hline_toroid}). + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/hline_zeros.png} + \caption{Работа автомата при нулевых граничных условиях и начальной конфигурации <<Горизонтальная палочка>>.} + \label{fig:hline_zeros} + \end{figure} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/hline_toroid.png} + \caption{Работа автомата при тороидальных граничных условиях и начальной конфигурации <<Горизонтальная палочка>>.} + \label{fig:hline_toroid} + \end{figure} + + \newpage + При задании начальной конфигурации <<Вертикальная палочка>> (см. Рис.~\ref{fig:vline_zeros_toroid}) и нулевых или тороидальных граничных условий палочка сначала раздваивается и расходится в стороны до границ сетки, потом обратно сдвигается на одну клетку к центру и зацикливается (см. Рис.~\ref{fig:vline_zeros_toroid}). + + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/vline_zeros_toroid.png} + \caption{Работа автомата при нулевых и тороидальных граничных условиях и начальной конфигурации <<Вертикальная палочка>>.} + \label{fig:vline_zeros_toroid} + \end{figure} + + При задании начальной конфигурации <<Квадратик>> (см. Рис.~\ref{fig:start_square}) или <<Единичное поле>> (см. Рис.~\ref{fig:start_ones}) и нулевых граничных условий автомат зацикливается после 18-ой итерации (см. Рис.~\ref{fig:square_zeros}). При этом паттерны перед зацикливанием отличаются для разных начальных конфигураций и выглядят случайными. + + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/square_zeros.png} + \caption{Зацикливание автомата при нулевых граничных условиях и начальной конфигурации <<Квадратик>> или <<Единичное поле>>.} + \label{fig:square_zeros} + \end{figure} + + \newpage + Также автомат был несколько раз запущен на том же размере сетки (5 x 5), нулевых начальных условиях и случайных начальных конфигурациях для большего числа итераций ($n=300$). Таким образом удалось обнаружить ещё несколько циклических паттернов, к которым сходится рассматриваемый автомат. На Рис.~\ref{fig:zeros_random} представлен пример достаточно короткого циклического паттерна, а на Рис.~\ref{fig:start_cycle_8} представлена конфигурация, которая повторяется снова каждые 8 итераций. + + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/zeros_random.png} + \caption{Один из циклических паттернов рассматриваемого автомата.} + \label{fig:zeros_random} + \end{figure} + + \begin{figure}[h!] + \centering + \includegraphics[width=0.14\linewidth]{img/start_cycle_8.png} + \caption{Пример конфигурации, повторяющейся каждые 8 итераций.} + \label{fig:start_cycle_8} + \end{figure} \subsection{Сходимость}