<s>
The	O
Pythagoras	B-Algorithm
tree	I-Algorithm
is	O
a	O
plane	O
fractal	B-Application
constructed	O
from	O
squares	O
.	O
</s>
<s>
If	O
the	O
largest	O
square	O
has	O
a	O
size	O
of	O
LL	O
,	O
the	O
entire	O
Pythagoras	B-Algorithm
tree	I-Algorithm
fits	O
snugly	O
inside	O
a	O
box	O
of	O
size	O
6L4L	O
.	O
</s>
<s>
The	O
finer	O
details	O
of	O
the	O
tree	O
resemble	O
the	O
Lévy	B-Algorithm
C	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
construction	O
of	O
the	O
Pythagoras	B-Algorithm
tree	I-Algorithm
begins	O
with	O
a	O
square	O
.	O
</s>
<s>
The	O
illustration	O
below	O
shows	O
the	O
first	O
few	O
iterations	B-Algorithm
in	O
the	O
construction	O
process	O
.	O
</s>
<s>
Iteration	B-Algorithm
n	O
in	O
the	O
construction	O
adds	O
2n	O
squares	O
of	O
area	O
,	O
for	O
a	O
total	O
area	O
of	O
1	O
.	O
</s>
<s>
However	O
,	O
some	O
of	O
the	O
squares	O
overlap	O
starting	O
at	O
the	O
order	O
5	O
iteration	B-Algorithm
,	O
and	O
the	O
tree	O
actually	O
has	O
a	O
finite	O
area	O
because	O
it	O
fits	O
inside	O
a	O
64	O
box	O
.	O
</s>
<s>
It	O
can	O
be	O
shown	O
easily	O
that	O
the	O
area	O
A	O
of	O
the	O
Pythagoras	B-Algorithm
tree	I-Algorithm
must	O
be	O
in	O
the	O
range	O
5	O
<	O
A	O
<	O
18	O
,	O
which	O
can	O
be	O
narrowed	O
down	O
further	O
with	O
extra	O
effort	O
.	O
</s>
<s>
An	O
interesting	O
set	O
of	O
variations	O
can	O
be	O
constructed	O
by	O
maintaining	O
an	O
isosceles	O
triangle	O
but	O
changing	O
the	O
base	O
angle	O
(	O
90	O
degrees	O
for	O
the	O
standard	O
Pythagoras	B-Algorithm
tree	I-Algorithm
)	O
.	O
</s>
<s>
The	O
first	O
overlap	O
occurs	O
at	O
the	O
fourth	O
iteration	B-Algorithm
.	O
</s>
<s>
The	O
Pythagoras	B-Algorithm
tree	I-Algorithm
was	O
first	O
constructed	O
by	O
Albert	O
E	O
.	O
Bosman	O
(	O
1891	O
–	O
1961	O
)	O
,	O
a	O
Dutch	O
mathematics	O
teacher	O
,	O
in	O
1942	O
.	O
</s>
