Self-Formation, Development and Reproduction of the Artificial Planar Systems

Stepas Janušonis; Vida Janušonienė

doi:10.4028/www.scientific.net/SSP.97-98.391

[113] M. Apter 5. 3. 1. Closed Topological System. The systems discussed above interact with certain sequences of external systems, i. e. a formation takes place in the systems open for information. In the case of the system open for topology the topology is transferred in consecutive order from external systems to a forming system. In case of the system open for parameter, the figures of the initial system go through a series of transformations partly caused by a sequence of external systems, excluding topology, partly - by changing structure of the forming systems: by configuration and arrangement of figures. Examination of the system closed for topology and parameter will be accomplished hereinafter. The system closed for information is not closed from the point of view of thermodynamics. It may be open for energy and/or substances, however an energy and substance are derived in a chaotic state with no structure in space and in time. As it has been discussed, a closed topological system does not interact with a medium or external systems in the examined interval of time. There we have a non-equilibrium system. On the other hand an examination of completely non-equilibrium systems has no practical sense as discussed above. We are interested in non-equilibrium systems, that are in equilibrium state in the initial phase and carry themselves to equilibrium state after having progressed to the point of given complexity. Thus what interests us most is an investigation including putting out from equilibrium state, an evolution process and the resting to equilibrium state. Thus we introduce the new useful concepts. A closed equilibrium topological system in the non-interacting medium is further called as an elementary system. The elementary system can obtain a very different structure. The system, including two equilibrium elementary systems in distance of radius R<� of neighbourhood of a Euclidean point and obtaining an non-equilibrium state is further referred to the initial system. The initial system can be realised when two elementary systems come into contact and form a non-equilibrium system. As a rule there are two kinds of elementary systems. One of them includes topology on the plane while the other one can include a set of homogeneous planes with different parameters. We will call an evolution of a closed system followed by increase of its complexity we will call development [101, 126, 118]. This concept shows a principle analogous to the evolution of the closed topological systems with development of living beings from germ (seed-corn, egg, embryo). We will go into different kinds of development systems. It is a pity that we are able to examine only random cases of the development results of which confirm rather the fact of existence of such systems rather than its detail examination. The undetermined class and general laws of development of such systems remain. No doubt the research cases are chosen not by chance. They are defined by the already known technological achievements [101, 126, 118] and by analogous with living nature. 5. 3. 2. Development of Single Topological System. Development of the topological system occurs as an evolution of the initial system followed by increase of its complexity when an object interacts with another object. Localisation of interactions in space and time are controlled by evolutionary object itself. Evolution continues on at finite interval of time. Therefore a system must be equilibrium before and retain after evolution. Title of Publication (to be inserted by the publisher) Let us have a topological space including a set of parameters P = {0, 1, .., 7}. (5. 27) Let us assume that there are two different elementary systems in the topological space (Fig. 5. 9., a, b).

Self-Formation, Development and Reproduction of the Artificial Planar Systems

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