This is a weakened version of Is the measure induced by the Mandelbrot set computable on rational rectangles? ;
Given a (computable, or rational) rectangle in the complex plane, is it computable whether:
- The rectangle is contained within the Mandelbrot set?
- The rectangle is disjoint from the Mandelbrot set?
The above-referenced question asked whether the measure of the intersection of a (computable) rectangle and the Mandelbrot set is computable.
Given a (computable) complex number, it is probably computable whether that number is in the Mandelbrot set, but I'm not even sure of that. If that is insoluble, it does not necessarily make my question (for an open rectangle) insoluble.