<s>
In	O
mathematics	O
,	O
in	O
the	O
study	O
of	O
fractals	B-Application
,	O
a	O
Hutchinson	B-Algorithm
operator	I-Algorithm
is	O
the	O
collective	O
action	O
of	O
a	O
set	O
of	O
contractions	O
,	O
called	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
.	O
</s>
<s>
The	O
iteration	B-Algorithm
of	O
the	O
operator	O
converges	O
to	O
a	O
unique	O
attractor	O
,	O
which	O
is	O
the	O
often	O
self-similar	O
fixed	O
set	O
of	O
the	O
operator	O
.	O
</s>
<s>
Let	O
be	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
,	O
or	O
a	O
set	O
of	O
contractions	O
from	O
a	O
compact	O
set	O
to	O
itself	O
.	O
</s>
<s>
The	O
proof	O
follows	O
by	O
showing	O
that	O
the	O
Hutchinson	B-Algorithm
operator	I-Algorithm
is	O
contractive	O
on	O
the	O
set	O
of	O
compact	O
subsets	O
of	O
in	O
the	O
Hausdorff	O
distance	O
.	O
</s>
<s>
With	O
N	O
functions	O
,	O
then	O
one	O
may	O
visualize	O
the	O
monoid	O
as	O
a	O
full	O
N-ary	B-Data_Structure
tree	I-Data_Structure
or	O
a	O
Cayley	B-Algorithm
tree	I-Algorithm
.	O
</s>
