fixed point, and hence usually referred to as the **basin of infinity**. In this case, is an open and connected subset of the complex plane, and the Julia set is the boundary of this basin. For instance the escaping set of the complex quadratic polynomial consists precisely of the complement of the closed unit disc: Transcendental entire functions For transcendental entire functions, the escaping set is much more complicated than for polynomials: in the simplest cases like the one illustrated in the picture it consists of uncountably many curves, called hairs or rays. In other examples the structure of the escaping set can be very different (a spider's web). As mentioned above, there are examples of transcendental entire functions whose escaping set contains no curves. By definition, the escaping set is an Fσδ set; that is, a countable intersection of Fσ sets. It is neither Gδ nor Fσ. See also escape condition or bailout target set Notes References External links Complex analysis