<s>
A	O
fractal	B-Algorithm
landscape	I-Algorithm
or	O
fractal	B-Algorithm
surface	I-Algorithm
is	O
generated	O
using	O
a	O
stochastic	O
algorithm	O
designed	O
to	O
produce	O
fractal	B-Application
behavior	O
that	O
mimics	O
the	O
appearance	O
of	O
natural	O
terrain	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
the	O
surface	O
resulting	O
from	O
the	O
procedure	O
is	O
not	O
a	O
deterministic	O
,	O
but	O
rather	O
a	O
random	O
surface	O
that	O
exhibits	O
fractal	B-Application
behavior	O
.	O
</s>
<s>
Many	O
natural	O
phenomena	O
exhibit	O
some	O
form	O
of	O
statistical	O
self-similarity	O
that	O
can	O
be	O
modeled	O
by	O
fractal	B-Algorithm
surfaces	I-Algorithm
.	O
</s>
<s>
Moreover	O
,	O
variations	O
in	O
surface	O
texture	O
provide	O
important	O
visual	O
cues	O
to	O
the	O
orientation	O
and	O
slopes	O
of	O
surfaces	O
,	O
and	O
the	O
use	O
of	O
almost	O
self-similar	O
fractal	B-Application
patterns	O
can	O
help	O
create	O
natural	O
looking	O
visual	O
effects	O
.	O
</s>
<s>
Because	O
the	O
intended	O
result	O
of	O
the	O
process	O
is	O
to	O
produce	O
a	O
landscape	O
,	O
rather	O
than	O
a	O
mathematical	O
function	O
,	O
processes	O
are	O
frequently	O
applied	O
to	O
such	O
landscapes	O
that	O
may	O
affect	O
the	O
stationarity	B-Algorithm
and	O
even	O
the	O
overall	O
fractal	B-Application
behavior	O
of	O
such	O
a	O
surface	O
,	O
in	O
the	O
interests	O
of	O
producing	O
a	O
more	O
convincing	O
landscape	O
.	O
</s>
<s>
The	O
first	O
use	O
of	O
a	O
fractal-generated	O
landscape	O
in	O
a	O
film	O
was	O
in	O
1982	O
for	O
the	O
movie	O
Star	O
Trek	O
II	O
:	O
The	O
Wrath	O
of	O
Khan.Loren	O
Carpenter	O
refined	O
the	O
techniques	O
of	O
Mandelbrot	O
to	O
create	O
an	O
alien	O
landscape	O
.	O
</s>
<s>
Whether	O
or	O
not	O
natural	O
landscapes	O
behave	O
in	O
a	O
generally	O
fractal	B-Application
manner	O
has	O
been	O
the	O
subject	O
of	O
some	O
research	O
.	O
</s>
<s>
Technically	O
speaking	O
,	O
any	O
surface	O
in	O
three-dimensional	O
space	O
has	O
a	O
topological	O
dimension	O
of	O
2	O
,	O
and	O
therefore	O
any	O
fractal	B-Algorithm
surface	I-Algorithm
in	O
three-dimensional	O
space	O
has	O
a	O
Hausdorff	O
dimension	O
between	O
2	O
and	O
3	O
.	O
</s>
<s>
This	O
means	O
that	O
an	O
attempt	O
to	O
calculate	O
the	O
'	O
overall	O
 '	O
fractal	B-Application
dimension	O
of	O
a	O
real	O
landscape	O
can	O
result	O
in	O
measures	O
of	O
negative	O
fractal	B-Application
dimension	O
,	O
or	O
of	O
fractal	B-Application
dimension	O
above	O
3	O
.	O
</s>
<s>
In	O
particular	O
,	O
many	O
studies	O
of	O
natural	O
phenomena	O
,	O
even	O
those	O
commonly	O
thought	O
to	O
exhibit	O
fractal	B-Application
behavior	O
,	O
do	O
not	O
do	O
so	O
,	O
over	O
more	O
than	O
a	O
few	O
orders	O
of	O
magnitude	O
.	O
</s>
<s>
For	O
instance	O
,	O
Richardson	O
's	O
examination	O
of	O
the	O
western	O
coastline	O
of	O
Britain	O
showed	O
fractal	B-Application
behavior	O
of	O
the	O
coastline	O
over	O
only	O
two	O
orders	O
of	O
magnitude	O
.	O
</s>
<s>
Real	O
landscapes	O
also	O
have	O
varying	O
statistical	O
behavior	O
from	O
place	O
to	O
place	O
,	O
so	O
for	O
example	O
sandy	O
beaches	O
do	O
n't	O
exhibit	O
the	O
same	O
fractal	B-Application
properties	O
as	O
mountain	O
ranges	O
.	O
</s>
<s>
A	O
fractal	B-Algorithm
function	I-Algorithm
,	O
however	O
,	O
is	O
statistically	O
stationary	O
,	O
meaning	O
that	O
its	O
bulk	O
statistical	O
properties	O
are	O
the	O
same	O
everywhere	O
.	O
</s>
<s>
Thus	O
,	O
any	O
real	O
approach	O
to	O
modeling	O
landscapes	O
requires	O
the	O
ability	O
to	O
modulate	O
fractal	B-Application
behavior	O
spatially	O
.	O
</s>
<s>
Additionally	O
real	O
landscapes	O
have	O
very	O
few	O
natural	O
minima	O
(	O
most	O
of	O
these	O
are	O
lakes	O
)	O
,	O
whereas	O
a	O
fractal	B-Algorithm
function	I-Algorithm
has	O
as	O
many	O
minima	O
as	O
maxima	O
,	O
on	O
average	O
.	O
</s>
<s>
Real	O
landscapes	O
also	O
have	O
features	O
originating	O
with	O
the	O
flow	O
of	O
water	O
and	O
ice	O
over	O
their	O
surface	O
,	O
which	O
simple	O
fractals	B-Application
cannot	O
model	O
.	O
</s>
<s>
It	O
is	O
because	O
of	O
these	O
considerations	O
that	O
the	O
simple	O
fractal	B-Algorithm
functions	I-Algorithm
are	O
often	O
inappropriate	O
for	O
modeling	O
landscapes	O
.	O
</s>
<s>
A	O
way	O
to	O
make	O
such	O
a	O
landscape	O
is	O
to	O
employ	O
the	O
random	B-Algorithm
midpoint	I-Algorithm
displacement	I-Algorithm
algorithm	I-Algorithm
,	O
in	O
which	O
a	O
square	O
is	O
subdivided	O
into	O
four	O
smaller	O
equal	O
squares	O
and	O
the	O
center	O
point	O
is	O
vertically	O
offset	O
by	O
some	O
random	O
amount	O
.	O
</s>
<s>
There	O
are	O
many	O
fractal	B-Application
procedures	O
(	O
such	O
as	O
combining	O
multiple	O
octaves	O
of	O
Simplex	O
noise	O
)	O
capable	O
of	O
creating	O
terrain	O
data	O
,	O
however	O
,	O
the	O
term	O
"	O
fractal	B-Algorithm
landscape	I-Algorithm
"	O
has	O
become	O
more	O
generic	O
over	O
time	O
.	O
</s>
<s>
Fractal	B-Application
plants	O
can	O
be	O
procedurally	O
generated	O
using	O
L-systems	B-Language
in	O
computer-generated	O
scenes	O
.	O
</s>
