Simulation of sandcastle lifetime based on cellular automata

Abstract

Every day, we look forward to vocations. During vocations, we can go to beach and enjoy interest that sea wave, sunshine and sand take to us. On almost every beach, there are people who make sandcastles out of the sand. These sandcastles are full of their enjoyment, happiness and imagination. In this paper, we discuss what 3-dimentional geometric shape of sand foundation can last longer on the beach, allowing those pleasures last longer. We discuss the optimal three-dimensional geometry of the sand base at the same sand-to-water mixture proportion using the same amount of sand. We set up a spatial rectangular coordinate system, and set up a surface equation to describe the top surface of the sand foundation. By integrating the surface function and restricting the sand volume, the relationship between the parameters in the equation is obtained. We use trigonometric models to describe the shape of waves. After discretize the space, a 3-dimensional cellular automata sandcastle simulation model is established by analyzing the stress of each cell. The computer program is used for analogue simulation and solving the model.