<s>
In	O
mathematics	O
the	O
Vicsek	B-Algorithm
fractal	I-Algorithm
,	O
also	O
known	O
as	O
Vicsek	B-Algorithm
snowflake	I-Algorithm
or	O
box	B-Algorithm
fractal	I-Algorithm
,	O
is	O
a	O
fractal	B-Application
arising	O
from	O
a	O
construction	O
similar	O
to	O
that	O
of	O
the	O
Sierpinski	O
carpet	O
,	O
proposed	O
by	O
Tamás	O
Vicsek	O
.	O
</s>
<s>
Box	B-Algorithm
fractal	I-Algorithm
also	O
refers	O
to	O
various	O
iterated	O
fractals	B-Application
created	O
by	O
a	O
square	O
or	O
rectangular	O
grid	O
with	O
various	O
boxes	O
removed	O
or	O
absent	O
and	O
,	O
at	O
each	O
iteration	O
,	O
those	O
present	O
and/or	O
those	O
absent	O
have	O
the	O
previous	O
image	O
scaled	O
down	O
and	O
drawn	O
within	O
them	O
.	O
</s>
<s>
The	O
Sierpinski	O
triangle	O
may	O
be	O
approximated	O
by	O
a	O
box	B-Algorithm
fractal	I-Algorithm
with	O
one	O
corner	O
removed	O
.	O
</s>
<s>
The	O
Sierpinski	O
carpet	O
is	O
a	O
box	B-Algorithm
fractal	I-Algorithm
with	O
the	O
middle	O
square	O
removed	O
.	O
</s>
<s>
The	O
Vicsek	B-Algorithm
fractal	I-Algorithm
is	O
the	O
set	O
obtained	O
at	O
the	O
limit	O
of	O
this	O
procedure	O
.	O
</s>
<s>
The	O
Hausdorff	O
dimension	O
of	O
this	O
fractal	B-Application
is	O
≈	O
1.46497	O
.	O
</s>
<s>
The	O
Vicsek	B-Algorithm
fractal	I-Algorithm
has	O
the	O
surprising	O
property	O
that	O
it	O
has	O
zero	O
area	O
yet	O
an	O
infinite	O
perimeter	B-Application
,	O
due	O
to	O
its	O
non-integer	O
dimension	O
.	O
</s>
<s>
The	O
perimeter	B-Application
however	O
is	O
,	O
because	O
each	O
side	O
is	O
divided	O
into	O
three	O
parts	O
and	O
the	O
center	O
one	O
is	O
replaced	O
with	O
three	O
sides	O
,	O
yielding	O
an	O
increase	O
of	O
three	O
to	O
five	O
.	O
</s>
<s>
The	O
perimeter	B-Application
approaches	O
infinity	O
as	O
n	O
increases	O
.	O
</s>
<s>
The	O
boundary	O
of	O
the	O
Vicsek	B-Algorithm
fractal	I-Algorithm
is	O
the	O
Type	O
1	O
quadratic	O
Koch	O
curve	O
.	O
</s>
<s>
There	O
is	O
a	O
three-dimensional	O
analogue	O
of	O
the	O
Vicsek	B-Algorithm
fractal	I-Algorithm
.	O
</s>
<s>
Similarly	O
to	O
the	O
two-dimensional	O
Vicsek	B-Algorithm
fractal	I-Algorithm
,	O
this	O
figure	O
has	O
zero	O
volume	O
.	O
</s>
<s>
There	O
exist	O
an	O
infinite	O
number	O
of	O
cross	B-Application
sections	I-Application
which	O
yield	O
the	O
two-dimensional	O
Vicsek	B-Algorithm
fractal	I-Algorithm
.	O
</s>
