Sandcastle stacking problem based on particle swarm algorithm

Abstract:
There are recreational sandy ocean beaches in the world, and children like to use their tools and imagination on the beach to create a variety of sandcastles. However, the waves often destroy their creative results. Consequently, one wonders if there exists a best 3-dimensional geometric shape to use for a sandcastle foundation. First, we use an analog cellular automaton to simulate the shape of the foundation, put all the sand in a spatial angle coordinate system, describe the geometric shape of the sand through the matrix, and establish its own sand model, we also simplified some forces between the sands. In the case of only considering sand, According to the force between the sand and the bonding effect of water on the sand, through the particle swarm optimization algorithm, we get the adhesion between water and sand particles and the optimal water-sand ratio: 0.8443.