This paper expounds the definition of the general Julia sets (they are called the general J sets for short) from the complex mappingz←zα+c(α<0). A series of interesting and rich families of fractal images are generated by changing a single parameterα. Whenαis a negative integer the fractal image has a planetary configuration consisting of a central planet with α major satellite structures. For noninteger values ofα

additional embryonic satellite structures

proportional in size to the fractional part ofα

are observed. Using the experimental mathematics method combining the theory of analytic function of one complex variable with computer aided drawing

we have analyzed the structural characteristics and the evolutions of the general J set for negative real index number. That the different evolution of the general J set results from the different choice of principal range for the phase angleθis found

and the four evolutions of the general J set are given for the first time.