The REAL generalized Mandelbrot set

f(a+ib) = (a+ib)^d+ik + C = (a+ib)ⁱ + C

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The minimum value of variable a
The maximum value of variable a
The minimum value of variable b
The maximum value of variable b
The real part of the exponent
The imaginary part of the exponent
Multiple of 2π to get extra solutions
This is another fifth dimensional axis
Julia Set parameter real part
Julia Set parameter imaginary part
increase / decrease : Axis: Conjugate: Burning Ship:

The case when f(a+ib)
Positive Integer Powers
Matching Integer Powers

The conjugate case when f(a-ib)
Positive Integer Powers
Matching Integer Powers

Testing Area
Testing Area Saved Images
Testing Area Matching Images

the idea of matching cases resembles and reminds me the analytic continuation of the Riemann zeta function!
Only here you are assigning an image instead of a value. The sets of the matching cases appear to have a circular perimeter
but this is because of the fixed maximum radius allowed by the escape time algorithm, and is not a limit of the sets!!!