<s>
The	O
Douady	B-Algorithm
rabbit	I-Algorithm
is	O
any	O
of	O
various	O
particular	O
filled	B-Algorithm
Julia	I-Algorithm
sets	I-Algorithm
whose	O
parameter	O
is	O
near	O
the	O
center	O
of	O
a	O
period	O
3	O
bud	O
of	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
for	O
complex	B-Algorithm
quadratic	I-Algorithm
map	I-Algorithm
.	O
</s>
<s>
The	O
rabbit	O
is	O
generated	O
by	O
iterating	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
map	O
on	O
the	O
complex	O
plane	O
with	O
fixed	O
to	O
lie	O
in	O
the	O
period	O
three	O
bulb	O
off	O
the	O
main	O
cardiod	O
and	O
ranging	O
over	O
the	O
plane	O
.	O
</s>
<s>
The	O
"	O
Douady	B-Algorithm
Rabbit	I-Algorithm
"	O
Julia	O
set	O
is	O
visible	O
in	O
the	O
cross	O
section	O
.	O
</s>
<s>
The	O
fat	B-Algorithm
rabbit	I-Algorithm
or	O
chubby	O
rabbit	O
has	O
c	O
at	O
the	O
root	O
of	O
1/3	O
-limb	O
of	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
.	O
</s>
<s>
It	O
has	O
a	O
parabolic	B-Algorithm
fixed	I-Algorithm
point	I-Algorithm
with	O
3	O
petals	O
.	O
</s>
<s>
There	O
are	O
two	O
common	O
forms	O
for	O
the	O
complex	B-Algorithm
quadratic	I-Algorithm
map	I-Algorithm
.	O
</s>
<s>
The	O
filled	B-Algorithm
Julia	I-Algorithm
set	I-Algorithm
consists	O
of	O
all	O
points	O
in	O
the	O
mapping	O
plane	O
whose	O
images	O
remain	O
bounded	O
under	O
indefinitely	O
repeated	O
applications	O
of	O
.	O
</s>
<s>
The	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
consists	O
of	O
those	O
points	O
in	O
the	O
control	O
plane	O
such	O
that	O
the	O
associated	O
filled	B-Algorithm
Julia	I-Algorithm
set	I-Algorithm
in	O
the	O
mapping	O
plane	O
is	O
connected	O
.	O
</s>
<s>
Figure	O
1	O
shows	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
when	O
is	O
the	O
control	O
parameter	O
,	O
and	O
Figure	O
2	O
shows	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
when	O
is	O
the	O
control	O
parameter	O
.	O
</s>
<s>
Since	O
and	O
are	O
affine	B-Algorithm
transformations	I-Algorithm
of	O
one	O
another	O
(	O
a	O
linear	O
transformation	O
plus	O
a	O
translation	O
)	O
,	O
the	O
filled	B-Algorithm
Julia	I-Algorithm
sets	I-Algorithm
look	O
much	O
the	O
same	O
in	O
either	O
the	O
or	O
planes	O
.	O
</s>
<s>
The	O
Douady	B-Algorithm
rabbit	I-Algorithm
is	O
most	O
easily	O
described	O
in	O
terms	O
of	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
as	O
shown	O
in	O
Figure	O
1	O
(	O
above	O
)	O
.	O
</s>
<s>
In	O
this	O
figure	O
,	O
the	B-Algorithm
Mandelbrot	I-Algorithm
set	I-Algorithm
,	O
at	O
least	O
when	O
viewed	O
from	O
a	O
distance	O
,	O
appears	O
as	O
two	O
back-to-back	O
unit	O
discs	O
with	O
sprouts	O
.	O
</s>
<s>
When	O
is	O
within	O
one	O
of	O
these	O
four	O
sprouts	O
,	O
the	O
associated	O
filled	B-Algorithm
Julia	I-Algorithm
set	I-Algorithm
in	O
the	O
mapping	O
plane	O
is	O
a	O
Douady	B-Algorithm
rabbit	I-Algorithm
.	O
</s>
<s>
Douady	B-Algorithm
's	I-Algorithm
rabbit	I-Algorithm
consists	O
of	O
the	O
three	O
attracting	O
fixed	O
points	O
,	O
,	O
and	O
and	O
their	O
basins	O
of	O
attraction	O
.	O
</s>
<s>
For	O
example	O
,	O
Figure	O
3	O
shows	O
Douady	B-Algorithm
's	I-Algorithm
rabbit	I-Algorithm
in	O
the	O
plane	O
when	O
,	O
a	O
point	O
in	O
the	O
five-o	O
'	O
clock	O
sprout	O
of	O
the	O
right	O
disk	O
.	O
</s>
<s>
As	O
a	O
second	O
example	O
,	O
Figure	O
4	O
shows	O
a	O
Douady	B-Algorithm
rabbit	I-Algorithm
when	O
,	O
a	O
point	O
in	O
the	O
eleven-o	O
'	O
clock	O
sprout	O
on	O
the	O
left	O
disk	O
.	O
</s>
