Collapsed sandcastle model based on cellular automata

Abstract

Based on cellular automata, the model of collapsed sandcastle can simulate the number of sand blocks falling. We assume that a part of the sand blocks disappear after each wave strikes the sandcastle. Meantime, due to the disappearance of the lower sand blocks, the upper sand blocks may collapse. We use cubes to simulate sand blocks and combine them into three-dimensional foundations of different shapes. We simulate the impact of triangle model, square model and octagon model with the same height and the same bottom area. By comparing the number of dropped squares, we guess that when the three-dimensional foundation is a cylinder, the number of sand blocks falling off is the least. In addition to considering the influence of the shape of the bottom, we also define the ratio of height to the length (or diameter) of the bottom kkCH . When the shape and volume of the bottom remain the same, kkCHdetermines the number of sand falling off. When kkCH = 1, the number of sand blocks falling off is the least. Finally, we summarize the paper: when the volume fraction of seawater is, the bottom of Sandberg tends to be round, and when kkCH = 1, the Sandberg is the most stable.