<s>
Gradient	B-Algorithm
pattern	I-Algorithm
analysis	I-Algorithm
(	O
GPA	O
)	O
is	O
a	O
geometric	O
computing	O
method	O
for	O
characterizing	O
geometrical	O
bilateral	O
symmetry	O
breaking	O
of	O
an	O
ensemble	O
of	O
symmetric	O
vectors	O
regularly	O
distributed	O
in	O
a	O
square	O
lattice	O
.	O
</s>
<s>
Usually	O
,	O
the	O
lattice	O
of	O
vectors	O
represent	O
the	O
first-order	O
gradient	O
of	O
a	O
scalar	O
field	O
,	O
here	O
an	O
M	O
x	O
M	O
square	O
amplitude	O
matrix	B-Architecture
.	O
</s>
<s>
An	O
important	O
property	O
of	O
the	O
gradient	O
representation	O
is	O
the	O
following	O
:	O
A	O
given	O
M	O
x	O
M	O
matrix	B-Architecture
where	O
all	O
amplitudes	O
are	O
different	O
results	O
in	O
an	O
M	O
x	O
M	O
gradient	O
lattice	O
containing	O
asymmetric	O
vectors	O
.	O
</s>
<s>
By	O
connecting	O
all	O
vectors	O
using	O
a	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
criterion	O
it	O
is	O
possible	O
to	O
characterize	O
gradient	O
asymmetries	O
computing	O
the	O
so-called	O
gradient	O
asymmetry	O
coefficient	O
,	O
that	O
has	O
been	O
defined	O
as	O
:	O
</s>
<s>
For	O
a	O
complex	O
extended	O
pattern	O
(	O
matrix	B-Architecture
of	O
amplitudes	O
of	O
a	O
spatio-temporal	O
pattern	O
)	O
composed	O
by	O
locally	O
asymmetric	O
fluctuations	O
,	O
is	O
nonzero	O
,	O
defining	O
different	O
classes	O
of	O
irregular	O
fluctuation	O
patterns	O
(	O
1/f	O
noise	O
,	O
chaotic	O
,	O
reactive-diffusive	O
,	O
etc	O
.	O
</s>
