Fractal model of “breakthrough” innovation in nanotechnology

Abstract

Abstract The fractal modeling approach is applied to the distribution process of breakthrough innovation in nanotechnology. For modeling, a diffusion-limited aggregation fractal is used. This model takes into account the change in the probability of adhesion (the ability to perceive innovations) and viscosity (the rate of propagation of innovations). Evaluation of the fractal dimension of the simulated structures allows us to identify trends and predict their further development. The model system reaches a breakthrough jump with a fractal dimension greater than 1.6. The unstable nature of the further development of the system will be observed with a sharp increase in fractal dimension, if the parameters of the ability to perceive innovations and the speed of innovation spread to level 1. Favorable conditions for the technological leap are realized in the case with a slightly lower fractal dimension when the rate of innovation spread is 1. The stable nature of the development of the system is observed at medium rates and above. With general trends below the average, the leap will be difficult to achieve.