Abstract
The paper focuses on analysing the computational time complexity of Frontal Cellular Automata (FCAs) and comparing it with Classic Cellular Automata (CCAs). Some variants of CCAs and FCAs are described and presented by showing differences in their structure and transition rules. Several variants of simple two-dimensional (2D) CAs and four variants of three-dimensional (3D) CAs for grain growth have been developed, tested and analysed. These four 3D CA algorithms are described. The calculation time of several simulation cases is measured for 2D and 3D CAs. The computational time complexity is determined on the basis of these measurements. The paper also takes into account the parallelisation of calculations with CAs. Time measurements show the possibility of accelerating the calculations. The paper also presents examples of the application of FCAs to solidification, recrystallisation, phase transformation and grain refinement with giving their simulation time. The computational complexity of different CAs is discussed, and FCAs with cells organised into linked lists show the lowest computational complexity. The paper ends with conclusions highlighting the low computational complexity and time efficiency of FCA.
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