<s>
In	O
mathematics	O
,	O
the	O
Lévy	B-Algorithm
C	I-Algorithm
curve	I-Algorithm
is	O
a	O
self-similar	O
fractal	B-Algorithm
curve	I-Algorithm
that	O
was	O
first	O
described	O
and	O
whose	O
differentiability	O
properties	O
were	O
analysed	O
by	O
Ernesto	O
Cesàro	O
in	O
1906	O
and	O
Georg	O
Faber	O
in	O
1910	O
,	O
but	O
now	O
bears	O
the	O
name	O
of	O
French	O
mathematician	O
Paul	O
Lévy	O
,	O
who	O
was	O
the	O
first	O
to	O
describe	O
its	O
self-similarity	O
properties	O
as	O
well	O
as	O
to	O
provide	O
a	O
geometrical	O
construction	O
showing	O
it	O
as	O
a	O
representative	O
curve	O
in	O
the	O
same	O
class	O
as	O
the	O
Koch	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
It	O
is	O
a	O
special	O
case	O
of	O
a	O
period-doubling	O
curve	O
,	O
a	O
de	B-Algorithm
Rham	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
If	O
using	O
a	O
Lindenmayer	B-Language
system	I-Language
then	O
the	O
construction	O
of	O
the	O
C	B-Algorithm
curve	I-Algorithm
starts	O
with	O
a	O
straight	O
line	O
.	O
</s>
<s>
This	O
L-system	B-Language
can	O
be	O
described	O
as	O
follows	O
:	O
</s>
<s>
The	O
fractal	B-Algorithm
curve	I-Algorithm
that	O
is	O
the	O
limit	O
of	O
this	O
"	O
infinite	O
"	O
process	O
is	O
the	O
Lévy	B-Algorithm
C	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
curve	O
resembles	O
the	O
finer	O
details	O
of	O
the	O
Pythagoras	B-Algorithm
tree	I-Algorithm
.	O
</s>
<s>
The	O
Hausdorff	O
dimension	O
of	O
the	O
C	B-Algorithm
curve	I-Algorithm
equals	O
2	O
(	O
it	O
contains	O
open	O
sets	O
)	O
,	O
whereas	O
the	O
boundary	O
has	O
dimension	O
about	O
1.9340	O
.	O
</s>
<s>
The	O
standard	O
C	B-Algorithm
curve	I-Algorithm
is	O
built	O
using	O
45°	O
isosceles	O
triangles	O
.	O
</s>
<s>
Variations	O
of	O
the	O
C	B-Algorithm
curve	I-Algorithm
can	O
be	O
constructed	O
by	O
using	O
isosceles	O
triangles	O
with	O
angles	O
other	O
than	O
45°	O
.	O
</s>
<s>
If	O
using	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
(	O
IFS	O
,	O
or	O
the	O
chaos	B-Algorithm
game	I-Algorithm
IFS-method	O
actually	O
)	O
,	O
then	O
the	O
construction	O
of	O
the	O
C	B-Algorithm
curve	I-Algorithm
is	O
a	O
bit	O
easier	O
.	O
</s>
<s>
It	O
will	O
need	O
a	O
set	O
of	O
two	O
"	O
rules	O
"	O
which	O
are	O
:	O
Two	O
points	O
in	O
a	O
plane	O
(	O
the	O
translators	O
)	O
,	O
each	O
associated	O
with	O
a	O
scale	B-Algorithm
factor	I-Algorithm
of	O
1/	O
.	O
</s>
<s>
This	O
set	O
will	O
iterate	B-Algorithm
a	O
point	O
 [ x , y ] 	O
from	O
randomly	O
choosing	O
any	O
of	O
the	O
two	O
rules	O
and	O
use	O
the	O
parameters	O
associated	O
with	O
the	O
rule	O
to	O
scale/rotate	O
and	O
translate	O
the	O
point	O
using	O
a	O
2D-transform	O
function	O
.	O
</s>
