<s>
In	O
mathematics	O
,	O
the	O
are	O
three	O
disjoint	B-Algorithm
connected	O
open	O
sets	O
of	O
the	O
plane	O
or	O
open	O
unit	O
square	O
with	O
the	O
counterintuitive	O
property	O
that	O
they	O
all	O
have	O
the	O
same	O
boundary	O
.	O
</s>
<s>
More	O
than	O
two	O
sets	O
with	O
the	O
same	O
boundary	O
are	O
said	O
to	O
have	O
the	O
Wada	B-Algorithm
property	I-Algorithm
;	O
examples	O
include	O
Wada	B-Algorithm
basins	I-Algorithm
in	O
dynamical	O
systems	O
.	O
</s>
<s>
The	O
lakes	B-Algorithm
of	I-Algorithm
Wada	I-Algorithm
were	O
introduced	O
by	O
,	O
who	O
credited	O
the	O
discovery	O
to	O
Takeo	O
Wada	O
.	O
</s>
<s>
The	O
Lakes	B-Algorithm
of	I-Algorithm
Wada	I-Algorithm
are	O
formed	O
by	O
starting	O
with	O
a	O
closed	O
unit	O
square	O
of	O
dry	O
land	O
,	O
and	O
then	O
digging	O
3	O
lakes	O
according	O
to	O
the	O
following	O
rule	O
:	O
</s>
<s>
After	O
an	O
infinite	O
number	O
of	O
days	O
,	O
the	O
three	O
lakes	O
are	O
still	O
disjoint	B-Algorithm
connected	O
open	O
sets	O
,	O
and	O
the	O
remaining	O
dry	O
land	O
is	O
the	O
boundary	O
of	O
each	O
of	O
the	O
3	O
lakes	O
.	O
</s>
<s>
Wada	B-Algorithm
basins	I-Algorithm
are	O
certain	O
special	O
basins	O
of	O
attraction	O
studied	O
in	O
the	O
mathematics	O
of	O
non-linear	O
systems	O
.	O
</s>
<s>
A	O
basin	O
having	O
the	O
property	O
that	O
every	O
neighborhood	O
of	O
every	O
point	O
on	O
the	O
boundary	O
of	O
that	O
basin	O
intersects	O
at	O
least	O
three	O
basins	O
is	O
called	O
a	O
Wada	B-Algorithm
basin	I-Algorithm
,	O
or	O
said	O
to	O
have	O
the	O
Wada	B-Algorithm
property	I-Algorithm
.	O
</s>
<s>
Unlike	O
the	O
Lakes	B-Algorithm
of	I-Algorithm
Wada	I-Algorithm
,	O
Wada	B-Algorithm
basins	I-Algorithm
are	O
often	O
disconnected	O
.	O
</s>
<s>
An	O
example	O
of	O
Wada	B-Algorithm
basins	I-Algorithm
is	O
given	O
by	O
the	O
Newton	B-Algorithm
fractal	I-Algorithm
describing	O
the	O
basins	O
of	O
attraction	O
of	O
the	O
Newton	O
–	O
Raphson	O
method	O
for	O
finding	O
the	O
roots	O
of	O
a	O
cubic	O
polynomial	O
with	O
distinct	O
roots	O
,	O
such	O
as	O
see	O
the	O
picture	O
.	O
</s>
<s>
In	O
chaos	O
theory	O
,	O
Wada	B-Algorithm
basins	I-Algorithm
arise	O
very	O
frequently	O
.	O
</s>
<s>
Usually	O
,	O
the	O
Wada	B-Algorithm
property	I-Algorithm
can	O
be	O
seen	O
in	O
the	O
basin	O
of	O
attraction	O
of	O
dissipative	O
dynamical	O
systems	O
.	O
</s>
<s>
But	O
the	O
exit	O
basins	O
of	O
Hamiltonian	O
systems	O
can	O
also	O
show	O
the	O
Wada	B-Algorithm
property	I-Algorithm
.	O
</s>
<s>
In	O
the	O
context	O
of	O
the	O
chaotic	O
scattering	O
of	O
systems	O
with	O
multiple	O
exits	O
,	O
basins	O
of	O
exits	O
show	O
the	O
Wada	B-Algorithm
property	I-Algorithm
.	O
</s>
<s>
has	O
shown	O
that	O
in	O
the	O
Hénon	B-Algorithm
–	I-Algorithm
Heiles	I-Algorithm
system	I-Algorithm
the	O
exit	O
basins	O
have	O
this	O
Wada	B-Algorithm
property	I-Algorithm
.	O
</s>
