<s>
In	O
mathematics	O
,	O
a	O
Multibrot	B-Algorithm
set	I-Algorithm
is	O
the	O
set	O
of	O
values	O
in	O
the	O
complex	O
plane	O
whose	O
absolute	O
value	O
remains	O
below	O
some	O
finite	O
value	O
throughout	O
iterations	O
by	O
a	O
member	O
of	O
the	O
general	O
monic	O
univariate	O
polynomial	O
family	O
of	O
recursions	O
.	O
</s>
<s>
The	O
name	O
is	O
a	O
portmanteau	O
of	O
multiple	O
and	O
Mandelbrot	B-Algorithm
set	I-Algorithm
.	O
</s>
<s>
The	O
same	O
can	O
be	O
applied	O
to	O
the	O
Julia	B-Language
set	I-Language
,	O
this	O
being	O
called	O
Multijulia	O
set	O
.	O
</s>
<s>
is	O
the	O
classic	O
Mandelbrot	B-Algorithm
set	I-Algorithm
from	O
which	O
the	O
name	O
is	O
derived	O
.	O
</s>
<s>
The	O
example	O
is	O
the	O
original	O
Mandelbrot	B-Algorithm
set	I-Algorithm
.	O
</s>
<s>
The	O
examples	O
for	O
are	O
often	O
called	O
multibrot	B-Algorithm
sets	I-Algorithm
.	O
</s>
<s>
When	O
d	O
is	O
negative	O
the	O
set	O
appears	O
to	O
surround	O
but	O
does	O
not	O
include	O
the	O
origin	O
,	O
However	O
this	O
is	O
just	O
an	O
artifact	O
of	O
the	O
fixed	O
maximum	O
radius	O
allowed	O
by	O
the	O
Escape	O
Time	O
algorithm	O
,	O
and	O
is	O
not	O
a	O
limit	O
of	O
the	O
sets	O
that	O
actually	O
have	O
a	O
shape	O
in	O
the	O
middle	O
with	O
an	O
no	O
hole	O
(	O
You	O
can	O
see	O
this	O
by	O
using	O
the	O
Lyapunov	O
exponent	O
[	O
No	O
hole	O
because	O
the	O
origin	O
diverges	O
to	O
undefined	O
not	O
infinity	B-Application
because	O
the	O
origin	O
{	O
0	O
or	O
0+0i}	O
taken	O
to	O
a	O
negative	O
power	O
becomes	O
undefined ]	O
)	O
.	O
</s>
<s>
The	O
sets	O
appear	O
to	O
have	O
a	O
circular	O
perimeter	O
,	O
however	O
this	O
is	O
just	O
an	O
artifact	O
of	O
the	O
fixed	O
maximum	O
radius	O
allowed	O
by	O
the	O
Escape	O
Time	O
algorithm	O
,	O
and	O
is	O
not	O
a	O
limit	O
of	O
the	O
sets	O
that	O
actually	O
extend	O
in	O
all	O
directions	O
to	O
infinity	B-Application
.	O
</s>
<s>
The	O
resulting	O
set	O
rises	O
vertically	O
from	O
the	O
origin	O
in	O
a	O
narrow	O
column	O
to	O
infinity	B-Application
.	O
</s>
<s>
The	O
first	O
prominent	O
bump	O
or	O
spike	O
is	O
seen	O
at	O
an	O
exponent	O
of	O
2	O
,	O
the	O
location	O
of	O
the	O
traditional	O
Mandelbrot	B-Algorithm
set	I-Algorithm
at	O
its	O
cross-section	O
.	O
</s>
<s>
thumb|Multibrot	O
rendered	O
with	O
real	O
value	O
along	O
horizontal	O
axis	O
and	O
exponent	O
along	O
vertical	O
axis	O
,	O
imaginary	O
value	O
fixed	O
at	O
zerothumb|Multibrot	O
rendered	O
with	O
imaginary	O
value	O
on	O
horizontal	O
axis	O
and	O
exponent	O
on	O
vertical	O
axis	O
,	O
real	O
value	O
fixed	O
at	O
zerothumb|Multibrot	O
rendered	O
with	O
exponent	O
on	O
vertical	O
axis	O
along	O
a	O
plane	O
angled	O
45-degrees	O
between	O
the	O
real	O
and	O
imaginary	O
axes	O
.	O
</s>
