Here we will play our program in three cases in non analytic way.

Case 1: The  "Mandelbrot set" is defined by P(z)=(x-i y)²+c. It is kind of antiholomorphic Mandelbrot set. It is interesting to observe that near the origin there is no dynamics, but there are three Mandelbrot-like sets symmetrically at the ends. Here is the program to play.

Note the program does not somehow popup in the size I wanted. Just resize it to your like.

Case 2: The  "Mandelbrot set" is defined by P(z)=z²+i y²+c. It is kind of non- holomorphic Mandelbrot set. It is interesting to observe that it  is  just like Mandelbrot set.. Here is the program to play.

Case 3: The  "Mandelbrot set" is defined by P(z)=z²+i x²+c. This time is not so lucky. It is interesting to observe that it  is nothing  like Mandelbrot set. Here is the program to play.

Is any math behind these cases? I don't know and want to know!