<s>
The	O
Barnsley	B-Algorithm
fern	I-Algorithm
is	O
a	O
fractal	B-Application
named	O
after	O
the	O
British	O
mathematician	O
Michael	O
Barnsley	O
who	O
first	O
described	O
it	O
in	O
his	O
book	O
Fractals	B-Application
Everywhere	O
.	O
</s>
<s>
Like	O
the	O
Sierpinski	O
triangle	O
,	O
the	O
Barnsley	B-Algorithm
fern	I-Algorithm
shows	O
how	O
graphically	O
beautiful	O
structures	O
can	O
be	O
built	O
from	O
repetitive	O
uses	O
of	O
mathematical	O
formulas	O
with	O
computers	O
.	O
</s>
<s>
Barnsley	O
's	O
1988	O
book	O
Fractals	B-Application
Everywhere	O
is	O
based	O
on	O
the	O
course	O
which	O
he	O
taught	O
for	O
undergraduate	O
and	O
graduate	O
students	O
in	O
the	O
School	O
of	O
Mathematics	O
,	O
Georgia	O
Institute	O
of	O
Technology	O
,	O
called	O
Fractal	B-Application
Geometry	O
.	O
</s>
<s>
After	O
publishing	O
the	O
book	O
,	O
a	O
second	O
course	O
was	O
developed	O
,	O
called	O
Fractal	B-Application
Measure	O
Theory	O
.	O
</s>
<s>
The	O
fern	O
code	O
developed	O
by	O
Barnsley	O
is	O
an	O
example	O
of	O
an	O
iterated	B-Algorithm
function	I-Algorithm
system	I-Algorithm
(	O
IFS	O
)	O
to	O
create	O
a	O
fractal	B-Application
.	O
</s>
<s>
Barnsley	B-Algorithm
's	I-Algorithm
fern	I-Algorithm
uses	O
four	O
affine	B-Algorithm
transformations	I-Algorithm
.	O
</s>
<s>
Barnsley	O
shows	O
the	O
IFS	O
code	O
for	O
his	O
Black	O
Spleenwort	O
fern	O
fractal	B-Application
as	O
a	O
matrix	O
of	O
values	O
shown	O
in	O
a	O
table	O
.	O
</s>
<s>
Though	O
Barnsley	B-Algorithm
's	I-Algorithm
fern	I-Algorithm
could	O
in	O
theory	O
be	O
plotted	O
by	O
hand	O
with	O
a	O
pen	O
and	O
graph	O
paper	O
,	O
the	O
number	O
of	O
iterations	O
necessary	O
runs	O
into	O
the	O
tens	O
of	O
thousands	O
,	O
which	O
makes	O
use	O
of	O
a	O
computer	O
practically	O
mandatory	O
.	O
</s>
<s>
Many	O
different	O
computer	O
models	O
of	O
Barnsley	B-Algorithm
's	I-Algorithm
fern	I-Algorithm
are	O
popular	O
with	O
contemporary	O
mathematicians	O
.	O
</s>
<s>
In	O
his	O
paper	O
on	O
V-variable	O
fractals	B-Application
,	O
Barnsley	O
calls	O
this	O
trait	O
a	O
superfractal	O
.	O
</s>
