<s>
The	O
Fibonacci	B-Algorithm
word	I-Algorithm
fractal	I-Algorithm
is	O
a	O
fractal	B-Algorithm
curve	I-Algorithm
defined	O
on	O
the	O
plane	O
from	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
.	O
</s>
<s>
This	O
curve	O
is	O
built	O
iteratively	O
by	O
applying	O
the	O
Odd	O
–	O
Even	O
Drawing	O
rule	O
to	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
0100101001001	O
...	O
:	O
</s>
<s>
To	O
a	O
Fibonacci	B-Algorithm
word	I-Algorithm
of	O
length	O
(	O
the	O
nth	O
Fibonacci	B-Algorithm
number	I-Algorithm
)	O
is	O
associated	O
a	O
curve	O
made	O
of	O
segments	O
.	O
</s>
<s>
Some	O
of	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
fractal	I-Algorithm
's	O
properties	O
include	O
:	O
</s>
<s>
The	O
number	O
of	O
self-similarities	O
at	O
level	O
n	O
is	O
a	O
Fibonacci	B-Algorithm
number	I-Algorithm
\−1	O
.	O
</s>
<s>
The	O
number	O
of	O
those	O
square	O
structures	O
is	O
a	O
Fibonacci	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
The	O
Hausdorff	O
dimension	O
of	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
fractal	I-Algorithm
is	O
,	O
with	O
the	O
golden	O
ratio	O
.	O
</s>
<s>
Exchanging	O
the	O
roles	O
of	O
"	O
0	O
"	O
and	O
"	O
1	O
"	O
in	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
,	O
or	O
in	O
the	O
drawing	O
rule	O
yields	O
a	O
similar	O
curve	O
,	O
but	O
oriented	O
45°	O
.	O
</s>
<s>
From	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
,	O
one	O
can	O
define	O
the	O
«	O
dense	O
Fibonacci	O
word»	O
,	O
on	O
an	O
alphabet	O
of	O
3	O
letters	O
:	O
102210221102110211022102211021102110221022102211021	O
...	O
.	O
</s>
<s>
It	O
is	O
conjectured	O
that	O
the	O
Fibonacci	B-Algorithm
word	I-Algorithm
fractal	I-Algorithm
appears	O
for	O
every	O
sturmian	O
word	O
for	O
which	O
the	O
slope	O
,	O
written	O
in	O
continued	O
fraction	O
expansion	O
,	O
ends	O
with	O
an	O
infinite	O
sequence	O
of	O
"	O
1	O
"	O
s	O
.	O
</s>
<s>
its	O
perimeter	B-Application
at	O
order	O
n	O
equals	O
,	O
where	O
is	O
the	O
nth	O
Fibonacci	B-Algorithm
number	I-Algorithm
.	O
</s>
