<s>
A	O
dragon	B-Algorithm
curve	I-Algorithm
is	O
any	O
member	O
of	O
a	O
family	O
of	O
self-similar	O
fractal	B-Algorithm
curves	I-Algorithm
,	O
which	O
can	O
be	O
approximated	O
by	O
recursive	O
methods	O
such	O
as	O
Lindenmayer	B-Language
systems	I-Language
.	O
</s>
<s>
The	O
dragon	B-Algorithm
curve	I-Algorithm
is	O
probably	O
most	O
commonly	O
thought	O
of	O
as	O
the	O
shape	O
that	O
is	O
generated	O
from	O
repeatedly	O
folding	O
a	O
strip	O
of	O
paper	O
in	O
half	O
,	O
although	O
there	O
are	O
other	O
curves	O
that	O
are	O
called	O
dragon	B-Algorithm
curves	I-Algorithm
that	O
are	O
generated	O
differently	O
.	O
</s>
<s>
The	O
Heighway	B-Algorithm
dragon	I-Algorithm
(	O
also	O
known	O
as	O
the	O
Harter	B-Algorithm
–	I-Algorithm
Heighway	I-Algorithm
dragon	I-Algorithm
or	O
the	O
Jurassic	O
Park	O
dragon	O
)	O
was	O
first	O
investigated	O
by	O
NASA	O
physicists	O
John	O
Heighway	O
,	O
Bruce	O
Banks	O
,	O
and	O
William	O
Harter	O
.	O
</s>
<s>
The	O
Heighway	B-Algorithm
dragon	I-Algorithm
can	O
be	O
constructed	O
from	O
a	O
base	O
line	O
segment	O
by	O
repeatedly	O
replacing	O
each	O
segment	O
by	O
two	O
segments	O
with	O
a	O
right	O
angle	O
and	O
with	O
a	O
rotation	O
of	O
45°	O
alternatively	O
to	O
the	O
right	O
and	O
to	O
the	O
left	O
:	O
</s>
<s>
The	O
Heighway	B-Algorithm
dragon	I-Algorithm
is	O
also	O
the	O
limit	O
set	O
of	O
the	O
following	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
in	O
the	O
complex	O
plane	O
:	O
</s>
<s>
The	O
Heighway	B-Algorithm
dragon	I-Algorithm
curve	I-Algorithm
can	O
be	O
constructed	O
by	O
folding	O
a	O
strip	O
of	O
paper	O
,	O
which	O
is	O
how	O
it	O
was	O
originally	O
discovered	O
.	O
</s>
<s>
the	O
second	O
iteration	O
of	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
.	O
</s>
<s>
Fold	O
the	O
strip	O
in	O
half	O
again	O
to	O
the	O
right	O
,	O
and	O
the	O
turn	O
sequence	O
of	O
the	O
unfolded	O
strip	O
is	O
now	O
RRLRRLL	O
–	O
the	O
third	O
iteration	O
of	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
.	O
</s>
<s>
Continuing	O
folding	O
the	O
strip	O
in	O
half	O
to	O
the	O
right	O
to	O
create	O
further	O
iterations	O
of	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
(	O
in	O
practice	O
,	O
the	O
strip	O
becomes	O
too	O
thick	O
to	O
fold	O
sharply	O
after	O
four	O
or	O
five	O
iterations	O
)	O
.	O
</s>
<s>
Many	O
self-similarities	O
can	O
be	O
seen	O
in	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
dragon	B-Algorithm
curve	I-Algorithm
can	O
tile	B-Algorithm
the	I-Algorithm
plane	I-Algorithm
.	O
</s>
<s>
One	O
possible	O
tiling	O
replaces	O
each	O
edge	O
of	O
a	O
square	O
tiling	O
with	O
a	O
dragon	B-Algorithm
curve	I-Algorithm
,	O
using	O
the	O
recursive	O
definition	O
of	O
the	O
dragon	O
starting	O
from	O
a	O
line	O
segment	O
.	O
</s>
<s>
As	O
a	O
non-self-crossing	O
space-filling	B-Algorithm
curve	I-Algorithm
,	O
the	O
dragon	B-Algorithm
curve	I-Algorithm
has	O
fractal	O
dimension	O
exactly	O
2	O
.	O
</s>
<s>
For	O
a	O
dragon	B-Algorithm
curve	I-Algorithm
with	O
initial	O
segment	O
length	O
1	O
,	O
its	O
area	O
is	O
1/2	O
,	O
as	O
can	O
be	O
seen	O
from	O
its	O
tilings	O
of	O
the	O
plane	O
.	O
</s>
<s>
The	O
twindragon	O
(	O
also	O
known	O
as	O
the	O
Davis	O
–	O
Knuth	O
dragon	O
)	O
can	O
be	O
constructed	O
by	O
placing	O
two	O
Heighway	B-Algorithm
dragon	I-Algorithm
curves	I-Algorithm
back	O
to	O
back	O
.	O
</s>
<s>
It	O
is	O
also	O
the	O
limit	O
set	O
of	O
the	O
following	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
:	O
</s>
<s>
It	O
can	O
be	O
also	O
written	O
as	O
a	O
Lindenmayer	B-Language
system	I-Language
–	O
it	O
only	O
needs	O
adding	O
another	O
section	O
in	O
initial	O
string	O
:	O
</s>
<s>
The	O
terdragon	O
can	O
be	O
written	O
as	O
a	O
Lindenmayer	B-Language
system	I-Language
:	O
</s>
<s>
It	O
is	O
the	O
limit	O
set	O
of	O
the	O
following	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
:	O
</s>
<s>
The	O
Lévy	B-Algorithm
C	I-Algorithm
curve	I-Algorithm
is	O
sometimes	O
known	O
as	O
the	O
Lévy	O
dragon	O
.	O
</s>
<s>
The	O
dragon	B-Algorithm
curve	I-Algorithm
belongs	O
to	O
a	O
basic	O
set	O
of	O
iteration	O
functions	O
consisting	O
of	O
two	O
lines	O
with	O
four	O
possible	O
orientations	O
at	O
perpendicular	O
angles	O
:	O
</s>
<s>
A	O
discrete	O
dragon	B-Algorithm
curve	I-Algorithm
can	O
be	O
converted	O
to	O
a	O
dragon	O
polyomino	O
as	O
shown	O
.	O
</s>
<s>
Like	O
discrete	O
dragon	B-Algorithm
curves	I-Algorithm
,	O
dragon	O
polyominoes	O
approach	O
the	O
fractal	B-Algorithm
dragon	I-Algorithm
curve	O
as	O
a	O
limit	O
.	O
</s>
<s>
This	O
is	O
similar	O
to	O
how	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
produces	O
new	O
points	O
in	O
a	O
set	O
,	O
though	O
not	O
all	O
IFS	O
are	O
linear	O
functions	O
.	O
</s>
<s>
It	O
can	O
be	O
seen	O
that	O
for	O
,	O
the	O
above	O
pair	O
of	O
functions	O
is	O
equivalent	O
to	O
the	O
IFS	O
formulation	O
of	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
.	O
</s>
<s>
That	O
is	O
,	O
the	O
Heighway	B-Algorithm
dragon	I-Algorithm
,	O
iterated	O
to	O
a	O
certain	O
iteration	O
,	O
describe	O
the	O
set	O
of	O
all	O
Littlewood	O
polynomials	O
up	O
to	O
a	O
certain	O
degree	O
,	O
evaluated	O
at	O
the	O
point	O
.	O
</s>
<s>
Indeed	O
,	O
when	O
plotting	O
a	O
sufficiently	O
high	O
number	O
of	O
roots	O
of	O
the	O
Littlewood	O
polynomials	O
,	O
structures	O
similar	O
to	O
the	O
dragon	B-Algorithm
curve	I-Algorithm
appear	O
at	O
points	O
close	O
to	O
these	O
coordinates	O
.	O
</s>
