<s>
In	O
mathematics	O
,	O
Lyapunov	B-Algorithm
fractals	I-Algorithm
(	O
also	O
known	O
as	O
Markus	O
–	O
Lyapunov	B-Algorithm
fractals	I-Algorithm
)	O
are	O
bifurcational	O
fractals	B-Application
derived	O
from	O
an	O
extension	O
of	O
the	O
logistic	B-Algorithm
map	I-Algorithm
in	O
which	O
the	O
degree	O
of	O
the	O
growth	O
of	O
the	O
population	O
,	O
r	O
,	O
periodically	O
switches	O
between	O
two	O
values	O
A	O
and	O
B	O
.	O
</s>
<s>
A	O
Lyapunov	B-Algorithm
fractal	I-Algorithm
is	O
constructed	O
by	O
mapping	O
the	O
regions	O
of	O
stability	O
and	O
chaotic	O
behaviour	O
(	O
measured	O
using	O
the	O
Lyapunov	O
exponent	O
)	O
in	O
the	O
ab	O
plane	O
for	O
given	O
periodic	O
sequences	O
of	O
a	O
and	O
b	O
.	O
</s>
<s>
Lyapunov	B-Algorithm
fractals	I-Algorithm
were	O
discovered	O
in	O
the	O
late	O
1980s	O
by	O
the	O
Germano-Chilean	O
physicist	O
Mario	O
Markus	O
from	O
the	O
Max	O
Planck	O
Institute	O
of	O
Molecular	O
Physiology	O
.	O
</s>
<s>
Lyapunov	B-Algorithm
fractals	I-Algorithm
are	O
generally	O
drawn	O
for	O
values	O
of	O
A	O
and	O
B	O
in	O
the	O
interval	O
.	O
</s>
<s>
In	O
practice	O
,	O
shifting	O
this	O
sequence	O
leads	O
to	O
changes	O
in	O
the	O
fractal	B-Application
,	O
as	O
some	O
branches	O
get	O
covered	O
by	O
others	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
Lyapunov	B-Algorithm
fractal	I-Algorithm
for	O
the	O
iteration	O
sequence	O
AB	O
(	O
see	O
top	O
figure	O
on	O
the	O
right	O
)	O
is	O
not	O
perfectly	O
symmetric	O
with	O
respect	O
to	O
a	O
and	O
b	O
.	O
</s>
<s>
The	O
algorithm	O
for	O
computing	O
Lyapunov	B-Algorithm
fractals	I-Algorithm
works	O
as	O
follows	O
:	O
</s>
<s>
Lyapunov	B-Algorithm
fractals	I-Algorithm
can	O
be	O
calculated	O
in	O
more	O
than	O
two	O
dimensions	O
.	O
</s>
<s>
The	O
sequence	O
string	O
for	O
a	O
n-dimensional	O
fractal	B-Application
has	O
to	O
be	O
built	O
from	O
an	O
alphabet	O
with	O
n	O
characters	O
,	O
e.g.	O
</s>
<s>
"	O
ABBBCA	O
"	O
for	O
a	O
3D	O
fractal	B-Application
,	O
which	O
can	O
be	O
visualized	O
either	O
as	O
3D	O
object	O
or	O
as	O
an	O
animation	O
showing	O
a	O
"	O
slice	O
"	O
in	O
the	O
C	O
direction	O
for	O
each	O
animation	O
frame	O
,	O
like	O
the	O
example	O
given	O
here	O
.	O
</s>
