Three Dimensional Cellular Automata Sand Castle construction Model Based on Step Factor

Abstract

It seems that everyone has the experience of making sandcastles on the leisure beach. In order to know how to build a beautiful and sturdy beach castle, this article simulates and analyzes the process of sand castles being eroded by water, and obtains some factors that extend the life of sand castles. First, we model the waves. Simplify the waves into a sine wave. Using calculus and fluid mechanics, the water wave impact force on a particle on the sand castle was calculated. Second, we model the sandcastle. Discretizing time, space, and state, we innovatively introduce the concepts of friction and impact into the model, and propose a new Three-dimensional Cellular Automaton model combined with step factors. We consider each gravel or water molecule as a cell, and simultaneously introduce the moving probability and collision probability to describe the moving trend and collision between the gravel cells, respectively. In order to effectively describe the loss of sand castles in the waves, the gravel cells that are in direct contact with the water cells will receive an impact force calculated by the first model. According to the law of large numbers, we use enough cells to simulate the erosion of sandcastles by the waves. It was found that within a certain range, the farther from the ocean and the more the total gravel, the stronger the anti-erosion ability of the sand castle.