<s>
A	O
Brownian	B-Algorithm
surface	I-Algorithm
is	O
a	O
fractal	B-Algorithm
surface	I-Algorithm
generated	O
via	O
a	O
fractal	B-Application
elevation	O
function	O
.	O
</s>
<s>
The	O
Brownian	B-Algorithm
surface	I-Algorithm
is	O
named	O
after	O
Brownian	O
motion	O
.	O
</s>
<s>
Efficient	O
generation	O
of	O
fractional	O
Brownian	B-Algorithm
surfaces	I-Algorithm
poses	O
significant	O
challenges	O
.	O
</s>
<s>
Since	O
the	O
Brownian	B-Algorithm
surface	I-Algorithm
represents	O
a	O
Gaussian	B-General_Concept
process	I-General_Concept
with	O
a	O
nonstationary	O
covariance	O
function	O
,	O
</s>
<s>
which	O
generates	O
an	O
auxiliary	O
stationary	O
Gaussian	B-General_Concept
process	I-General_Concept
using	O
the	O
circulant	O
embedding	O
approach	O
and	O
then	O
adjusts	O
this	O
auxiliary	O
process	O
to	O
obtain	O
the	O
desired	O
nonstationary	O
Gaussian	B-General_Concept
process	I-General_Concept
.	O
</s>
<s>
The	O
figure	O
below	O
shows	O
three	O
typical	O
realizations	O
of	O
fractional	O
Brownian	B-Algorithm
surfaces	I-Algorithm
for	O
different	O
values	O
of	O
the	O
roughness	O
or	O
Hurst	B-Algorithm
parameter	I-Algorithm
.	O
</s>
<s>
The	O
Hurst	B-Algorithm
parameter	I-Algorithm
is	O
always	O
between	O
zero	O
and	O
one	O
,	O
with	O
values	O
closer	O
to	O
one	O
corresponding	O
to	O
smoother	O
surfaces	O
.	O
</s>
