Pictures of Julia and Mandelbrot Sets/Favourite formulas

If you insert a random complex rational function in a fractal program, it is very unlikely that you will find an interesting locality in the Mandelbrot set. But sometimes you will witness a startling spectacle when you zoom in. And this is usually where two domains of different structures meet each other.

If you come across an interesting formula, then let the rest of us see it. You can here write the formula and the coordinates of the locality, and show a picture. You should also state the critical points, however you can neglect this, if you use ∞ and a real point of smallest numerical value, or if you (in case of iterations towards finite cycles) use two conjugate complex numbers of largest distance.

You should fell free to remove formulas that clearly have been surpassed by others.


 * $$z^2/2 + z^4/4 + c$$ c = (0.7, 1.3)
 * $$1 - z^2 + z^5/(2 + 4z) + c$$ c = (-0.163, 0.085)