Abstract
Mandelbrot set, which was provided as a highlight in fractal and chaos, is studied by many researchers. With the extension of Mandelbrot set to generalized [Formula: see text] set with different kinds of exponent [Formula: see text] ([Formula: see text] set), properties are hard to understand when [Formula: see text] is a complex number. In this paper, fractal property of generalized [Formula: see text] set with complex exponent [Formula: see text] is studied. First, a relation is constructed between generalized [Formula: see text] set with complex and real exponent. Then, distribution of [Formula: see text] set on complex plane is researched. Meanwhile, symmetry of generalized [Formula: see text] set is proved. Finally, graphics, generated by escape time algorithm, are the validated results of this paper.
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