<s>
In	O
complex	O
analysis	O
,	O
domain	B-Application
coloring	I-Application
or	O
a	O
color	O
wheel	O
graph	B-Application
is	O
a	O
technique	O
for	O
visualizing	O
complex	O
functions	O
by	O
assigning	O
a	O
color	O
to	O
each	O
point	O
of	O
the	O
complex	O
plane	O
.	O
</s>
<s>
By	O
assigning	O
points	O
on	O
the	O
complex	O
plane	O
to	O
different	O
colors	O
and	O
brightness	O
,	O
domain	B-Application
coloring	I-Application
allows	O
for	O
a	O
function	O
from	O
the	O
complex	O
plane	O
to	O
itself	O
—	O
whose	O
graph	B-Application
would	O
normally	O
require	O
four	O
space	O
dimensions	O
—	O
to	O
be	O
easily	O
represented	O
and	O
understood	O
.	O
</s>
<s>
A	O
graph	B-Application
of	O
a	O
real	O
function	O
can	O
be	O
drawn	O
in	O
two	O
dimensions	O
because	O
there	O
are	O
two	O
represented	O
variables	O
,	O
and	O
.	O
</s>
<s>
One	O
way	O
to	O
achieve	O
that	O
is	O
with	O
a	O
Riemann	O
surface	O
,	O
but	O
another	O
method	O
is	O
by	O
domain	B-Application
coloring	I-Application
.	O
</s>
<s>
A	O
common	O
practice	O
is	O
to	O
represent	O
the	O
complex	O
argument	O
,	O
,	O
(	O
also	O
known	O
as	O
"	O
phase	O
"	O
or	O
"	O
angle	O
"	O
)	O
with	O
a	O
hue	B-Language
following	O
the	O
color	O
wheel	O
,	O
and	O
the	O
magnitude	O
by	O
other	O
means	O
,	O
such	O
as	O
brightness	O
or	O
saturation	O
.	O
</s>
<s>
The	O
following	O
example	O
colors	O
the	O
origin	O
in	O
black	O
,	O
in	O
green	O
,	O
in	O
magenta	B-Algorithm
,	O
and	O
a	O
point	O
at	O
infinity	O
in	O
white	O
:	O
</s>
<s>
This	O
approach	O
uses	O
the	O
HSL	O
(	O
hue	B-Language
,	O
saturation	O
,	O
lightness	O
)	O
color	O
model	O
.	O
</s>
<s>
Vivid	O
colors	O
of	O
the	O
rainbow	O
are	O
rotating	O
in	O
a	O
continuous	O
way	O
on	O
the	O
complex	O
unit	O
circle	O
,	O
so	O
the	O
sixth	O
roots	O
of	O
unity	O
(	O
starting	O
with	O
1	O
)	O
are	O
:	O
green	O
,	O
cyan	O
,	O
blue	O
,	O
magenta	B-Algorithm
,	O
red	O
,	O
and	O
yellow	O
.	O
</s>
<s>
Since	O
the	O
HSL	O
color	B-Algorithm
space	I-Algorithm
is	O
not	O
perceptually	O
uniform	O
,	O
one	O
can	O
see	O
streaks	O
of	O
perceived	O
brightness	O
at	O
yellow	O
,	O
cyan	O
,	O
and	O
magenta	B-Algorithm
(	O
even	O
though	O
their	O
absolute	O
values	O
are	O
the	O
same	O
as	O
red	O
,	O
green	O
,	O
and	O
blue	O
)	O
and	O
a	O
halo	O
around	O
.	O
</s>
<s>
More	O
modern	O
color	B-Algorithm
spaces	I-Algorithm
,	O
e.g	O
,	O
the	O
Lab	O
color	B-Algorithm
space	I-Algorithm
or	O
CIECAM02	O
,	O
correct	O
this	O
,	O
making	O
the	O
images	O
more	O
accurate	O
and	O
less	O
saturated	O
.	O
</s>
<s>
This	O
is	O
done	O
for	O
a	O
variety	O
of	O
reasons	O
such	O
as	O
showing	O
more	O
detail	O
or	O
highlighting	O
certain	O
aspects	O
of	O
a	O
function	O
,	O
like	O
level	B-Algorithm
sets	I-Algorithm
.	O
</s>
<s>
Therefore	O
,	O
in	O
functions	O
that	O
have	O
large	O
ranges	O
of	O
magnitude	O
,	O
changes	O
in	O
magnitude	O
can	O
sometimes	O
be	O
hard	O
to	O
differentiate	O
when	O
a	O
very	O
large	O
change	O
is	O
also	O
pictured	O
in	O
the	O
graph	B-Application
.	O
</s>
<s>
In	O
the	O
graph	B-Application
on	O
the	O
right	O
,	O
these	O
discontinuities	O
occur	O
in	O
circles	O
around	O
the	O
center	O
,	O
and	O
show	O
a	O
dimming	O
of	O
the	O
graph	B-Application
that	O
can	O
then	O
start	O
becoming	O
brighter	O
again	O
.	O
</s>
<s>
A	O
similar	O
color	O
function	O
has	O
been	O
used	O
for	O
the	O
graph	B-Application
on	O
top	O
of	O
the	O
article	O
.	O
</s>
<s>
Discontinuities	O
may	O
be	O
placed	O
where	O
outputs	O
have	O
a	O
certain	O
property	O
to	O
highlight	O
which	O
parts	O
of	O
the	O
graph	B-Application
have	O
that	O
property	O
.	O
</s>
<s>
For	O
instance	O
,	O
a	O
graph	B-Application
may	O
instead	O
of	O
showing	O
the	O
color	O
cyan	O
jump	O
from	O
green	O
to	O
blue	O
.	O
</s>
<s>
Discontinuities	O
may	O
also	O
affect	O
large	O
portions	O
of	O
a	O
graph	B-Application
,	O
such	O
as	O
a	O
graph	B-Application
where	O
the	O
color	O
wheel	O
divides	O
the	O
graph	B-Application
into	O
quadrants	O
.	O
</s>
<s>
The	O
term	O
"	O
domain	B-Application
coloring	I-Application
"	O
was	O
coined	O
by	O
Frank	O
Farris	O
,	O
possibly	O
around	O
1998	O
.	O
</s>
<s>
There	O
were	O
many	O
earlier	O
uses	O
of	O
color	O
to	O
visualize	O
complex	O
functions	O
,	O
typically	O
mapping	O
argument	O
(	O
phase	O
)	O
to	O
hue	B-Language
.	O
</s>
<s>
People	O
who	O
experience	O
color	O
blindness	O
may	O
have	O
trouble	O
interpreting	O
such	O
graphs	O
when	O
they	O
are	O
made	O
with	O
standard	O
color	B-Algorithm
maps	I-Algorithm
.	O
</s>
<s>
This	O
issue	O
can	O
possibly	O
be	O
ameliorated	O
by	O
creating	O
alternate	O
versions	O
using	O
color	B-Algorithm
maps	I-Algorithm
that	O
fit	O
within	O
the	O
color	B-Algorithm
space	I-Algorithm
discernible	O
to	O
those	O
with	O
color	O
blindness	O
.	O
</s>
