Iterative patterns can be described by the component pattern of iteration and their way of connection for iteration. It is shown that the shape of the component pattern can be a rectangle for any iterative pattern, which is called a tile. The tile is related to the basis of the parallel translation group of the iterative pattern. The component pattern itself is identified by a "tessera" which is defined by a non-degenerate colored tile. The tessera is a compact representation of iterative patterns. Some natures of tesseras and tiles are also discussed. The number of the kinds of distinct iterative patterns for each way of iteration is evaluated.

The flexible network is a network composed of flexible logical multivalued cells which can be adjusted at will to perform any functions. The network is assumed to have a fixed interconnection pattern and to have a fixed-input variable assignment. We have already investigated the necessary and sufficient range of flexibility of the cell's function to obtain all the output functions the network could realize. Let the network be composed of p cells and let the necesary and sufficient flexibility range of the 1th cell be denoted by φζ for ζ = 1,...,p It is shown that although the range of flexibility of the whole network φ1X ... X φpis sufficient for the network, as a whole, to produce all the output functions the network could realize, the above range is not necessary in general. Finally we derive a sufficient condition for the proposition that the range of logical flexibility of the network, φ1X ...φp, is critical. This gives a relationship between the range of logical flexibility obtained by considering a cell in the network and the one obtained by considering the whole network.

The flexible network is a network composed of flexible logical multivalued cells that can be adjusted at will to perform any functions. The network is assumed to have a fixed-interconnection pattern and to have a fixed-input variable assignment. The following question is answered. What is the necessary and sufficient range of the flexibility of the cells' functions to obtain all the output functions the circuit could realize? Furthermore, the relation between the cells functions that realize the same output functions is derived and the number of different realizable output functions is counted.