Spine
The most studied polynomials are probably those of the form, which are often denoted by, where is any complex number. In this case, the spine of the filled Julia set is defined as arc between -fixed point and ,
with such properties:
- spine lies inside . This makes sense when is connected and full
- spine is invariant under 180 degree rotation,
- spine is a finite topological tree,
- Critical point always belongs to the spine.
- -fixed point is a landing point of external ray of angle zero ,
- is landing point of external ray .
Algorithms for constructing the spine:
- detailed version is described by A. Douady
- Simplified version of algorithm:
- connect and within by an arc,
- when has empty interior then arc is unique,
- otherwise take the shortest way that contains .
Curve :
divides dynamical plane into two components.
Read more about this topic: Filled Julia Set
Famous quotes containing the word spine:
“Much of a man’s character will be found betokened in his backbone. I would rather feel your spine than your skull, whoever you are. A thin joist of a spine never yet upheld a full and noble soul.”
—Herman Melville (1819–1891)