Growth and development of continuous structures

The artificial cell introduced here represents an extendedthree-dimensional linear hexahedral finite element. Each cell can sense two types of quantities which control growth and development of the structure, one refers to mechanical stress and the otherrefers to the morphogen diffusion level. These two qualities have proven to have crucial effects on the growth oforganisms~\cite{Lars2007,dickinson1999}\@. The stresses refer to the point inside the cell with the maximum principal stress. The three principal stresses are normalized by the yield stress of the material, and are identified in the genome with the letters\emph{a}, \emph{b}, \emph{c}\@. Their corresponding principaldirections are identified in the genome with the letters \emph{d},\emph{e}, \emph{f}\@. There are two kinds of morphogens, one is amorphogen corresponding to a point load in space that is to be supported; the other is a morphogen corresponding to the ground. Each morphogen diffuses through space through the cell walls with acorresponding direction and intensity (gradient)\@. These two quantities are identified in the genome with the letters \emph{h}and \emph{i} respectively. Rules (or words) are composed of genes.The model contains three kinds of genes.allThe first areconditional genes \emph{V}, \emph{W} which suppress gene activity.The second and the third are operation or transformation genes. Operation genes correspond to geometrical operations which change the shape of the cell (\emph{C},\emph{B},\emph{S}), and cell-typeoperations which divide or kill cells (\emph{D},\emph{K})\@.Transformation genes change the mechanical properties of the cell(\emph{F})\@.