@b4c50e1b IIRC when I played around with drawing this fractal some years ago, I didn't calculate roots of polynomials at a fixed degree, but eliminated regions (pixels) that couldn't possibly contain a root of any series extended from a given finite prefix (with the number of distinct prefixes limited in practice by GPU memory).

I have no idea if this approach generates the same mathematical object in the limit, but it looked similar to my eyes.

https://code.mathr.co.uk/littlewood has probably bitrotted 

 @cd2b7137 - a bunch of theorems are known for the set consisting of all roots of Littlewood polynomials of *all* degrees, and we discuss them in our paper, but in our pictures we lazily plotted pictures of roots of Littlewood polynomials of degree 23, so 24 nonzero terms, since any root of a Littlewood polynomial with n nonzero terms is also a root of one with m nonzero terms if n divides m. 

 @b4c50e1b @cd2b7137 Do the boundaries look similar for littlewood polynomials of all degrees? 

 @0bacad63 - of course they don't look similar for very small degrees, but by what I said the sets of roots converge as the degrees get large in the funny sense I described.

@cd2b7137 

 @b4c50e1b @cd2b7137 Thanks! that's what I meant - was making sure that as the degrees get large, the boundaries of the dragon-y shapes, for instance continue to look dragon-y as opposed to completely filling the space as it appears to closer to the |z|=1 regions 

 @0bacad63 - the sets do converge as the degrees get large (i.e. the degrees plus 1 get large in a multiplicative sense) , but a lot has not been proved about what the limiting set looks like!   

It's known that this set is contained in the annulus 

1 ≤ |z| ≤ 2 

and that it contains the annulus

2^(-1/4) ≤ |z| ≤ 2^(1/4)

It's also known that this set is connected and locally path-connected!  But that's about all.