Code to visually explore Generalized J Set with Escape-time algorithm iterating z<-z^p+c where p and c are parameters.
The images can be classified w.r.t. Re and Im values of c or Magnitute and Angle of c. Animations are made, and they are to be uploaded.
For what is meant by J-Set, see wikipedia "Julia Set".
A more technical intro can be found at http://mathworld.wolfram.com/JuliaSet.html
From web search (I haven't read technical proof of which) a pair of G. J sets are symmetrical about the Real axis if values for p are equal and values for c are symmertrical about the real axis on the complex plane.
see: (zh:广义Julia集关于迭代参数的对称性分析) Qin Xuanyun, Guan Jihong Ren Bo Han Xuli Analysis for the Symmetry of General J Sets to Iterated Parameters, Journal of Computer-Aided Design & Computer Graphics July 2017 (19) p 927-930
Floating number computation in such large scale takes time. I have estimated that to run the code will take around 10^2 days on my laptop (however this cannot be true as I have to use it for other things).