### The quadratic polynomial f_{1/4}

f_{1/4}is the quadratic ploynomical f(z) = z

^{2}+ c, where c≈ -0.228155 + 1.11514 i is a zero of the cubic polynomial c

^{3}+ 2c

^{2}+ 2c + 2.

The notation f

_{1/4}comes from external rays. In the complement of the filled Julia sets, the external ray with angle 1/4 (mod 1) lands at the critical value c. From this it follows that f(c) has angle 1/2 = 2 x 1/4, and f

^{2}(c) has angle 1 = 2 x 1/2. Since 2 x 1 ≡ 1 (mod 1), f

^{2}(c) is fixed and f has four postcritical points (∞, c, f(c), and f

^{2}(c). The Julia set for f

_{1/4}is shown in the figure below, which was created from Mathematica.

The diagram for f

_{1/4}