A fast algorithm for generating fractals

With iterated function systems (IFS), there are two classical algorithms of generating artificial fractal pictures: the deterministic algorithm and the random iteration algorithm. The deterministic algorithm spends huge computations on checking convergence iteratively. On the other hand, the random iteration algorithm is nondeterministic and time consuming. People seldom check convergence by the algorithm. Moreover, many pixels in the picture are computed again and again by both of the algorithms. Thus a new algorithm is given. The algorithm promises convergence without iterative checks. Also, our algorithm runs faster than the existing algorithms do on a large scale