<s>
In	O
mathematics	O
,	O
the	O
complex	B-Algorithm
squaring	I-Algorithm
map	I-Algorithm
,	O
a	O
polynomial	O
mapping	O
of	O
degree	O
two	O
,	O
is	O
a	O
simple	O
and	O
accessible	O
demonstration	O
of	O
chaos	O
in	O
dynamical	O
systems	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
angle	O
is	O
transformed	O
according	O
to	O
the	O
dyadic	B-Algorithm
transformation	I-Algorithm
(	O
also	O
known	O
as	O
the	O
2x	B-Algorithm
mod	I-Algorithm
1	I-Algorithm
map	I-Algorithm
)	O
.	O
</s>
<s>
As	O
the	O
initial	O
value	O
z0	O
has	O
been	O
chosen	O
so	O
that	O
its	O
argument	O
is	O
not	O
a	O
rational	O
multiple	O
of	O
π	O
,	O
the	O
forward	B-Algorithm
orbit	I-Algorithm
of	O
zn	O
cannot	O
repeat	O
itself	O
and	O
become	O
periodic	O
.	O
</s>
<s>
This	O
map	O
is	O
a	O
special	O
case	O
of	O
the	O
complex	B-Algorithm
quadratic	I-Algorithm
map	I-Algorithm
,	O
which	O
has	O
exact	O
solutions	O
for	O
many	O
special	O
cases	O
.	O
</s>
<s>
In	O
the	O
case	O
p	O
=	O
2	O
,	O
the	O
dynamics	O
can	O
be	O
mapped	O
to	O
the	O
dyadic	B-Algorithm
transformation	I-Algorithm
,	O
as	O
described	O
above	O
,	O
but	O
for	O
p>2	O
,	O
we	O
obtain	O
a	O
shift	O
map	O
in	O
the	O
number	O
basep	O
.	O
</s>
