Two dimensional ultradiscretization of the KPZ equation - Javellana, Lee (College of Engineering, University of the Philippines Diliman, 2018)
There are many mathematical models which are used to capture complex systems found in nature, one category of these models are the cellular automata. Cellular automata were thought to be inadequate to model complex systems due to the simple rules and discrete values. Recent researches have proven otherwise and more and more researchers have looked at cellular automata as an alternative method to model complex systems. The main drawback of using a cellular automaton to model a complex system is how to create the rules but the research of Tokihiro, Takahashi, Matsukidaira, and Satsuma showed that the rules of a cellular automaton can be derived from a continuous equation. The equations derived from these continuous equations which are used as the basic rules for a cellular automaton are called "ul tradiscrete equations". This research studied the derivation of the one dimensional ultradiscrete KPZ equation and was able to derive a two dimensional version of the ultradiscrete KPZ equation which were used to create a cellular automaton. The 1D and 2D cellular automata were run on different experimental scenarios and the pattern formed by the 2D cellular automaton is similar to the pattern created by the 1D version. From these results it can be said that the 2D cellular automaton is analogous to the 1D cellular automaton.