Automatic generating machines of patterns

Many methods of image generation being mainly intended for the realism of images, this pattern generation is a very different graphic generation from them. It is a trial for a sort of graphic art by using a machine. The equipments with machines are mainly composed of a mathematical model which may be constructed by computer programs or switching and other electric circuits. The model, called commutative linear representation systems (CLRS), is suitable for computer programs and electric circuits for linear operations. It has been already shown that there are relations between the index of CLRS and pattern with periodicity. In this paper, basic systems are introduced with the fact that any finite-sized pattern can be represented by them. And any pattern with periodicity can be represented as direct sum of minimum CLRS, which are called quasi-reachable basic system