Regarding the following picture on the Wikipedia article for Algebraic numbers:
The description is:
Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate degree of the polynomial the number is a root of (red = linear, i.e. the rationals, green = quadratic, blue = cubic, yellow = quartic...). Points becomes smaller as the integer polynomial coefficients become larger. View shows integers 0,1 and 2 at bottom right, +i near top.
If I understand it correctly, for each pixel $(x,y) \in \mathbb{Z}^2$, let $c = x+i y \in \mathbb{C}.$ The color is a mapping of $\deg(\mathrm{minpoly}(c))$.
If this is the case, then isn't the $\deg(\mathrm{minpoly}(c)) \le 2$ for all $c \in \mathbb{C}?$ Why does the picture has more colors? I think I misunderstood the picture description. What does this plot show?
Here is the WP talk page for the picture, and if relevant, here is the source code.