FRACTAL IMAGES OF GENERALIZED JULIA SETS

The iteration function z(n+1) = z(n)(alpha+i beta) + c, where both alp ha and beta are positive real numbers, is used to generate families of the generalized Julia sets, J(alpha,beta). The calculations are restr icted to the principal value of z(alpha+i beta) and the obtained resul ts demonstrate that classical Julia sets, J(2, 0), are significantly d eformed when non-zero values of beta are considered. As a result of th is deformation, the area of stable regions in the complex plane change s and a process of splitting and shifting takes place along the real a xis. It is shown that this process is responsible for the formation of new fractal images of generalized Julia sets.