<s>
The	O
Mandelbulb	B-Algorithm
is	O
a	O
three-dimensional	O
fractal	B-Application
,	O
constructed	O
for	O
the	O
first	O
time	O
in	O
1997	O
by	O
Jules	O
Ruis	O
and	O
in	O
2009	O
further	O
developed	O
by	O
Daniel	O
White	O
and	O
Paul	O
Nylander	O
using	O
spherical	O
coordinates	O
.	O
</s>
<s>
A	O
canonical	O
3-dimensional	O
Mandelbrot	B-Algorithm
set	I-Algorithm
does	O
not	O
exist	O
,	O
since	O
there	O
is	O
no	O
3-dimensional	O
analogue	O
of	O
the	O
2-dimensional	O
space	O
of	O
complex	O
numbers	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
construct	O
Mandelbrot	B-Algorithm
sets	I-Algorithm
in	O
4	O
dimensions	O
using	O
quaternions	O
and	O
bicomplex	O
numbers	O
.	O
</s>
<s>
The	O
Mandelbulb	B-Algorithm
is	O
then	O
defined	O
as	O
the	O
set	O
of	O
those	O
in	O
for	O
which	O
the	O
orbit	O
of	O
under	O
the	O
iteration	O
is	O
bounded	O
.	O
</s>
<s>
For	O
n>3	O
,	O
the	O
result	O
is	O
a	O
3-dimensional	O
bulb-like	O
structure	O
with	O
fractal	B-Application
surface	O
detail	O
and	O
a	O
number	O
of	O
"	O
lobes	O
"	O
depending	O
on	O
n	O
.	O
Many	O
of	O
their	O
graphic	O
renderings	O
use	O
n	O
=	O
8	O
.	O
</s>
<s>
This	O
reduces	O
to	O
the	O
complex	O
fractal	B-Application
when	O
z	O
=	O
0	O
and	O
when	O
y	O
=	O
0	O
.	O
</s>
<s>
Another	O
way	O
to	O
create	O
Mandelbulbs	B-Algorithm
with	O
cubic	O
symmetry	O
is	O
by	O
taking	O
the	O
complex	O
iteration	O
formula	O
for	O
some	O
integer	O
m	O
and	O
adding	O
terms	O
to	O
make	O
it	O
symmetrical	O
in	O
3	O
dimensions	O
but	O
keeping	O
the	O
cross-sections	O
to	O
be	O
the	O
same	O
2-dimensional	O
fractal	B-Application
.	O
</s>
<s>
for	O
arbitrary	O
constants	O
A	O
,	O
B	O
,	O
C	O
and	O
D	O
,	O
which	O
give	O
different	O
Mandelbulbs	B-Algorithm
(	O
usually	O
set	O
to	O
0	O
)	O
.	O
</s>
<s>
The	O
case	O
gives	O
a	O
Mandelbulb	B-Algorithm
most	O
similar	O
to	O
the	O
first	O
example	O
,	O
where	O
n	O
=	O
9	O
.	O
</s>
<s>
This	O
fractal	B-Application
has	O
cross-sections	O
of	O
the	O
power-9	O
Mandelbrot	B-Algorithm
fractal	I-Algorithm
.	O
</s>
<s>
The	O
cubic	O
fractal	B-Application
above	O
is	O
an	O
example	O
.	O
</s>
<s>
In	O
the	O
2014	O
computer-animated	O
film	O
Big	O
Hero	O
6	O
,	O
the	O
climax	O
takes	O
place	O
in	O
the	O
middle	O
of	O
a	O
wormhole	O
,	O
which	O
is	O
represented	O
by	O
the	O
stylized	O
interior	O
of	O
a	O
Mandelbulb	B-Algorithm
.	O
</s>
<s>
In	O
the	O
2018	O
science	O
fiction	O
horror	O
film	O
Annihilation	O
,	O
an	O
extraterrestrial	O
being	O
appears	O
in	O
the	O
form	O
of	O
a	O
partial	O
Mandelbulb	B-Algorithm
.	O
</s>
<s>
In	O
the	O
webcomic	O
Unsounded	O
the	O
spirit	O
realm	O
of	O
the	O
kerht	O
is	O
represented	O
by	O
a	O
stylized	O
golden	O
mandelbulb	B-Algorithm
.	O
</s>
