We need to construct the typical figure you get when plotting the roots of several Littlewood polynomials ($=$polynomials with coefficients $+1$ or $-1$) up to a certain degree. We need to solve this problem the other way around, so for a given $z$, is there a Littlewood polynomial which has that $z$ approximate as a root.
So in short, we need to find a Littlewood polynomial that has a given $z$ as an (approximate) root.
I guess the solution should be iterative.
Using this method should be more efficient to plot all the roots of the littlewoodpolynomials up to a given degree. So I think for plotting the roots in an efficient way, you should iterate over the complex plane (for example between the boundaries -2,2 for both x and y), calculate if there exists a littlewood polynomial with the given point as a root and based on that decide if you draw the point or not.
Anyone knows how to start or solve this problem?