The airplane

The airplane, the corabbit, and the rabbit (or Douady's rabbit) are quadratic polynomials f(z) = z2 + c, where c is a zero of the cubic polynomial c3 + 2c2 + c + 1. For the airplane c≈ -1.75488, for the corabbit c ≈ - 0.122561 - 0.744862 i, and for the rabbit c ≈ - 0.122561 + 0.744862 i.

The Julia set for the airplane is shown in the figure below, which was created from Mathematica.

The diagram for the airplane map

Input and output files