Fractal Images from z <- z a + c In the Complex z-Plane

Description

The transformation function z <- z[superscript a] + c is used for generating fractal images in the complex z-plane. When a is a positive integer the fractal image has a lobular structure with a major lobes. When a is a negative integer the image has a planetary configuration consisting of a central planet with | a | major satellite structures. For non-integer values of a, additional embryonic lobular/satellite structures, proportional in size to the fractional part of a, 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.