The conventional iteration algorithm for generareing fractal images is in the complex plane.In this paper we define a fractal quasi-hologram and present a rendering method based on the hypercomplex number system for generating fractal quasi-holograms in more than four dimensions. The results indicate that the Mandelbrot and Julia sets are fractal and symmetrical in these higher dimensions. The fractal quasi-holograms can also be used in laser anti-counterfeiting field.