Morphogenetic evolution of 3D sheets exploiting a spatial constraint

In this paper we show how geometric constraints enable developmental processes to generate the morphology of three-dimensional folding sheets more easily. These sheets consist of artificial cells, which are connected and are able to exert forces on each other. To keep track of the complex pattern of connectivity, we introduce a cell connection map, which represents the internal states of the cells and is used to visualize these states. The performed simulations show that the system can easily produce some complicated morphogenetic forms and we show that the forms can be quantified as entropy by evaluating the cell connection map. This entropy was also used as a fitness function in order to evolve shapes. We would like to point out that once an adequate geometric constraint is given, the forms are generated by simple internal states and cell-cell interactions.