Editing Dragon curve (section)

== Twindragon ==
[[File:Twindragon.png|thumb|Twindragon curve constructed from two Heighway dragons]]{{See also|Complex-base system#Base −1 ± i}}
The '''twindragon''' (also known as the '''Davis–Knuth dragon''') can be constructed by placing two Heighway dragon curves back to back (after flipping the original dragon curve vertically and horizontally). It is also the limit set of the following iterated function system:

:<math>f_1(z)=\frac{(1+i)z}{2}</math>
:<math>f_2(z)=1-\frac{(1+i)z}{2}</math>

where the initial shape is defined by the following set <math>S_0 = \{0,1,1-i\}</math>.

It can be also written as a [[Lindenmayer system]] – it only needs adding another section in the initial string:
* angle 90°
* initial string ''FX+FX+''
* string rewriting rules
** ''X'' {{mapsto}} ''X''+''YF''
** ''Y'' {{mapsto}} ''FX''−''Y''.
It is also the locus of points in the complex plane with the same integer part when written in [[Complex-base system#Base −1 ± i|base <math>(-1 \pm i)</math>]].<ref name="Knuth2">{{cite book |last=Knuth |first=Donald |title=The art of computer programming |publisher=Addison-Wesley |year=1998 |isbn=0-201-89684-2 |edition=3rd |volume=2 |location=Boston |pages=206 |chapter=Positional Number Systems |oclc=48246681 |authorlink=Donald Knuth}}</ref>