Abstract
The transformation function z ← z α + c is used for generating fractal images in the complex z-plane. When α is a positive integer the fractal image has a lobular structure with α major lobes. When α is a negative integer the image has a planetary configuration consisting of a central planet with | α| major satellite structures. For noninteger values of α, additional embryonic lobular/satellite structures, proportional in size to the fractional part of α, are observed. Based on the extensive experimentation, six conjectures regarding the number of major as well as embryonic lobular/satellite structures, their positions, and angular spaces are formulated.
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