<s>
In	O
mathematics	O
,	O
the	O
term	O
chaos	B-Algorithm
game	I-Algorithm
originally	O
referred	O
to	O
a	O
method	O
of	O
creating	O
a	O
fractal	B-Application
,	O
using	O
a	O
polygon	B-General_Concept
and	O
an	O
initial	O
point	O
selected	O
at	O
random	O
inside	O
it	O
.	O
</s>
<s>
The	O
fractal	B-Application
is	O
created	O
by	O
iteratively	O
creating	O
a	O
sequence	O
of	O
points	O
,	O
starting	O
with	O
the	O
initial	O
random	O
point	O
,	O
in	O
which	O
each	O
point	O
in	O
the	O
sequence	O
is	O
a	O
given	O
fraction	O
of	O
the	O
distance	O
between	O
the	O
previous	O
point	O
and	O
one	O
of	O
the	O
vertices	O
of	O
the	O
polygon	B-General_Concept
;	O
the	O
vertex	O
is	O
chosen	O
at	O
random	O
in	O
each	O
iteration	O
.	O
</s>
<s>
Repeating	O
this	O
iterative	O
process	O
a	O
large	O
number	O
of	O
times	O
,	O
selecting	O
the	O
vertex	O
at	O
random	O
on	O
each	O
iteration	O
,	O
and	O
throwing	O
out	O
the	O
first	O
few	O
points	O
in	O
the	O
sequence	O
,	O
will	O
often	O
(	O
but	O
not	O
always	O
)	O
produce	O
a	O
fractal	B-Application
shape	O
.	O
</s>
<s>
The	O
term	O
has	O
been	O
generalized	O
to	O
refer	O
to	O
a	O
method	O
of	O
generating	O
the	O
attractor	O
,	O
or	O
the	O
fixed	O
point	O
,	O
of	O
any	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
(	O
IFS	O
)	O
.	O
</s>
<s>
The	O
"	O
chaos	B-Algorithm
game	I-Algorithm
"	O
method	O
plots	O
points	O
in	O
random	O
order	O
all	O
over	O
the	O
attractor	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
other	O
methods	O
of	O
drawing	O
fractals	B-Application
,	O
which	O
test	O
each	O
pixel	O
on	O
the	O
screen	O
to	O
see	O
whether	O
it	O
belongs	O
to	O
the	O
fractal	B-Application
.	O
</s>
<s>
The	O
general	O
shape	O
of	O
a	O
fractal	B-Application
can	O
be	O
plotted	O
quickly	O
with	O
the	O
"	O
chaos	B-Algorithm
game	I-Algorithm
"	O
method	O
,	O
but	O
it	O
may	O
be	O
difficult	O
to	O
plot	O
some	O
areas	O
of	O
the	O
fractal	B-Application
in	O
detail	O
.	O
</s>
<s>
With	O
the	O
aid	O
of	O
the	O
"	O
chaos	B-Algorithm
game	I-Algorithm
"	O
a	O
new	O
fractal	B-Application
can	O
be	O
made	O
and	O
while	O
making	O
the	O
new	O
fractal	B-Application
some	O
parameters	O
can	O
be	O
obtained	O
.	O
</s>
<s>
These	O
parameters	O
are	O
useful	O
for	O
applications	O
of	O
fractal	B-Application
theory	O
such	O
as	O
classification	O
and	O
identification	O
.	O
</s>
<s>
The	O
new	O
fractal	B-Application
is	O
self-similar	O
to	O
the	O
original	O
in	O
some	O
important	O
features	O
such	O
as	O
fractal	B-Application
dimension	O
.	O
</s>
<s>
If	O
the	O
chaos	B-Algorithm
game	I-Algorithm
is	O
run	O
with	O
a	O
square	O
,	O
no	O
fractal	B-Application
appears	O
and	O
the	O
interior	O
of	O
the	O
square	O
fills	O
evenly	O
with	O
points	O
.	O
</s>
<s>
However	O
,	O
if	O
restrictions	O
are	O
placed	O
on	O
the	O
choice	O
of	O
vertices	O
,	O
fractals	B-Application
will	O
appear	O
in	O
the	O
square	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
the	O
current	O
vertex	O
cannot	O
be	O
chosen	O
in	O
the	O
next	O
iteration	O
,	O
this	O
fractal	B-Application
appears	O
:	O
</s>
<s>
If	O
the	O
current	O
vertex	O
cannot	O
be	O
one	O
place	O
away	O
(	O
anti-clockwise	O
)	O
from	O
the	O
previously	O
chosen	O
vertex	O
,	O
this	O
fractal	B-Application
appears	O
:	O
</s>
<s>
If	O
the	O
point	O
is	O
prevented	O
from	O
landing	O
on	O
a	O
particular	O
region	O
of	O
the	O
square	O
,	O
the	O
shape	O
of	O
that	O
region	O
will	O
be	O
reproduced	O
as	O
a	O
fractal	B-Application
in	O
other	O
and	O
apparently	O
unrestricted	O
parts	O
of	O
the	O
square	O
.	O
</s>
<s>
Here	O
,	O
for	O
example	O
,	O
is	O
the	O
fractal	B-Application
produced	O
when	O
the	O
point	O
cannot	O
jump	O
so	O
as	O
to	O
land	O
on	O
a	O
red	O
Om	O
symbol	O
at	O
the	O
center	O
of	O
the	O
square	O
:	O
</s>
<s>
When	O
the	O
length	O
of	O
the	O
jump	O
towards	O
a	O
vertex	O
or	O
another	O
point	O
is	O
not	O
1/2	O
,	O
the	O
chaos	B-Algorithm
game	I-Algorithm
generates	O
other	O
fractals	B-Application
,	O
some	O
of	O
them	O
very	O
well-known	O
.	O
</s>
<s>
For	O
example	O
,	O
when	O
the	O
jump	O
is	O
2/3	O
and	O
the	O
point	O
can	O
also	O
jump	O
towards	O
the	O
center	O
of	O
the	O
square	O
,	O
the	O
chaos	B-Algorithm
game	I-Algorithm
generates	O
the	O
Vicsek	B-Algorithm
fractal	I-Algorithm
:	O
</s>
<s>
When	O
the	O
jump	O
is	O
2/3	O
and	O
the	O
point	O
can	O
also	O
jump	O
towards	O
the	O
midpoints	O
of	O
the	O
four	O
sides	O
,	O
the	O
chaos	B-Algorithm
game	I-Algorithm
generates	O
the	O
Sierpinski	O
carpet	O
:	O
</s>
<s>
When	O
the	O
jump	O
is	O
1/phi	O
and	O
the	O
point	O
is	O
jumping	O
at	O
random	O
towards	O
one	O
or	O
another	O
of	O
the	O
five	O
vertices	O
of	O
a	O
regular	O
pentagon	O
,	O
the	O
chaos	B-Algorithm
game	I-Algorithm
generates	O
a	O
pentagonal	O
n-flake	B-Algorithm
:	O
</s>
