<s>
In	O
fractal	O
geometry	O
,	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
(	O
OSC	O
)	O
is	O
a	O
commonly	O
imposed	O
condition	O
on	O
self-similar	O
fractals	O
.	O
</s>
<s>
Specifically	O
,	O
given	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
of	O
contractive	O
mappings	O
,	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
requires	O
that	O
there	O
exists	O
a	O
nonempty	O
,	O
open	O
set	O
V	O
satisfying	O
two	O
conditions	O
:	O
</s>
<s>
Introduced	O
in	O
1946	O
by	O
P.A.P	O
Moran	O
,	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
is	O
used	O
to	O
compute	O
the	O
dimensions	O
of	O
certain	O
self-similar	O
fractals	O
,	O
notably	O
the	O
Sierpinski	O
Gasket	O
.	O
</s>
<s>
An	O
equivalent	O
statement	O
of	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
is	O
to	O
require	O
that	O
the	O
s-dimensional	O
Hausdorff	O
measure	O
of	O
the	O
set	O
is	O
greater	O
than	O
zero	O
.	O
</s>
<s>
When	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
holds	O
and	O
each	O
is	O
a	O
similitude	O
(	O
that	O
is	O
,	O
a	O
composition	O
of	O
an	O
isometry	O
and	O
a	O
dilation	O
around	O
some	O
point	O
)	O
,	O
then	O
the	O
unique	O
fixed	O
point	O
of	O
is	O
a	O
set	O
whose	O
Hausdorff	O
dimension	O
is	O
the	O
unique	O
solution	O
for	O
s	O
of	O
the	O
following	O
:	O
</s>
<s>
The	O
strong	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
(	O
SOSC	O
)	O
is	O
an	O
extension	O
of	O
the	O
open	B-Algorithm
set	I-Algorithm
condition	I-Algorithm
.	O
</s>
