Filled Julia set

The filled-in Julia set formula_1 of a polynomial formula_2 is :
Formal definition.
The filled-in Julia set formula_1 of a polynomial formula_2 is defined as the set of all points formula_5 of the dynamical plane that have bounded orbit with respect to formula_2
formula_7
<br>
where :
formula_8 is the set of complex numbers
formula_9 is the formula_10 -fold composition of formula_11 with itself = iteration of function formula_11
Relation to the Fatou set.
The filled-in Julia set is the (absolute) complement of the attractive basin of infinity. 
formula_13
The attractive basin of infinity is one of the components of the Fatou set.
formula_14
In other words, the filled-in Julia set is the complement of the unbounded Fatou component: 
formula_15
Relation between Julia, filled-in Julia set and attractive basin of infinity.
The Julia set is the common boundary of the filled-in Julia set and the attractive basin of infinity <br>
formula_16
where: 
formula_17 denotes the attractive basin of infinity = exterior of filled-in Julia set = set of escaping points for formula_11
formula_19
If the filled-in Julia set has no interior then the Julia set coincides with the filled-in Julia set. This happens when all the critical points of formula_11 are pre-periodic. Such critical points are often called Misiurewicz points.
Spine.
The most studied polynomials are probably those of the form formula_21, which are often denoted by formula_22, where formula_23 is any complex number. In this case, the spine formula_24 of the filled Julia set formula_25 is defined as arc between formula_26-fixed point and formula_27,
formula_28
with such properties:
Algorithms for constructing the spine:
Curve formula_41:
formula_42
divides dynamical plane into two components.