General Mandelbrot Sets Generated by the Complex Iteration z_(n+1)=_n~m+c
Zhu Zhi · Journal of Northeastern University · 2000
The general Mandelbrot sets generated by z n+1 = m n+c were studied. The Mandelbrot sets proved to be symmetrical by reflection of the real axis, and to have m+1 -way of rotationally symmetric. The stability condition of periodic orbits and the boundary curve of stability region of 1-periodic orbit were given, and the general Mandelbrot sets were constructed by the escape time method and the periodic scanning algorithm. These methods present a better understanding of the structure of the Mandelbrot sets.