Comment by ttoinou

My favorite alternative to Mandelbrot is the Monkelbrot, I made this 13 years ago (probably I discovered this formula on the old fractalforums.com)

https://www.deviantart.com/titoinou/art/The-42-MonkelBrot-29...

  f(z) = ( (z*c-1)^2 - 1 )^2 - 1 

It features Classic Quadratic Mandelbrots z^2 and also Quartic Brots z^4 in one set, that is apparently connected (I didn't prove this yet...). Also, it doesn't go crazy like others alternative, it stays nicely behaved like the original Mandelbrot set. You can copy paste "( (z*c-1)^2 - 1 )^2 - 1" without the quotes on this site to explore the fractal

It's really fascinating when navigating the fractal to try to understand where would a z^2 minibrot appear vs. where would a z^4 minibrot appear