Dynamic fractals in spatial evolutionary games
We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases
We investigate geometrical aspects of a spatial evolutionary game. The game is based on the Prisoner's dilemma. We analyze the geometrical structure of the space distribution of cooperators and defectors in the steady-state regime of evolution. We develop algorithm for the identification of the interfaces between clusters of cooperators and defectors, and measure fractal properties of the interfaces.
The article examines the relationship between power resource and rational behavior in history. It is shown that personal interest is expressed in socially useful economic activities of individuals only if they had no adequate power potential. This general principle is illustrated by examples of Russian medieval history that are associated with the specifics of the trade route «from the Varangians to the Greeks», with land ownership and changing social structure. Further the thesis of the strengthening of the connection between economy and power potential that helps to explain changes in the distribution of power, institutions and economic growth in the Western world in Modern history is elaborated and illustrated. Moreover, the author describes the social dynamics in situations when low social classes expand at social bottoms and, using their monopoly there, exalt.
A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).