Algorithmic growth and the inclusion of principles from quantum theory in cellular automata

We study forms that grow in cellular automata The algorithm that is proposed can have relevance in order to obtain representations useful for cognitive systems that model growth Also, it may shed tight on processes in external reality itself such as on the interplay between indeterminism and structure, and on non-reductionist growth. At every time step, the algorithm adds a single cell to a form. The selection of the new cell occurs in accordance with an amplitude function. Like in quantum theory, an amplitude is accompanied by a phase, and phase differences can generate constructive and destructive interference. These phenomena can control, among others, the degree of branching that occurs in a form, and they can constrain the places where points ate added when cycles of growth follow one another. The phase variable is a temporal variable; the amplitude in a cell depends on the extent to which a small template can be locally recognized in the form and on the local density. During a cycle of growth, different elementary templates may be used successively, and different cycles may follow one another. The process of growth can be constrained by affine transformations such as the scalings and symmetries that are familiar from IFS fractals. If the density of a form or part of it on a global scale is allowed to influence the type of indeterminism on the local scale, one obtains a non-reductionist dynamics that on be illustrated in visually appealing ways. The relevance of the present methods for computer generated art is pointed out and some general problems in complexity are addressed