Abstract: The complex mapping z←z w+c,（w=α+iβ,α,β∈R 1 ） is used to construct many J fractal images. For w=α＜0 , the Julia fractal images which are different from those in references concerned are generated. Based on a great number of experiments, an M J conjecture and a formula PNO for investigating corresponding relationship between the M set in the C plane and J set in the Z plane are presented to predict the image features of the J fractal image for a parameter c in the M set.