Directed control for fractal growth with environmental disturbance
环境干扰下分形生长的定方位控制

For a complex and disordered system of real fractal growth, the control model of the directed growth of the fractal growth with environmental disturbance is studied. Being different from the past studies on directed growth of the fractal growth based on their experiments, this work is concerned with the directed growth of the fractal growth theoretically. By the norm theory, we obtain a quantitative method for controlling the growing particles to aggregate in different regions when the environmental disturbance is a generalized function. The directed growth problem with the environmental disturbance in a more general functional form is solved by using the above obtained control method. Two examples of disturbances in quadratic polynomial and sinusoidal function are given, respectively. Simulation results illustrate that the growing particles will aggregate into the controlled regions when the corresponding controlled methods for associated growth regions are applied.