<s>
A	O
Moore	B-Algorithm
curve	I-Algorithm
(	O
after	O
E	O
.	O
H	O
.	O
Moore	O
)	O
is	O
a	O
continuous	O
fractal	B-Algorithm
space-filling	B-Algorithm
curve	I-Algorithm
which	O
is	O
a	O
variant	O
of	O
the	O
Hilbert	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
Precisely	O
,	O
it	O
is	O
the	O
loop	O
version	O
of	O
the	O
Hilbert	B-Algorithm
curve	I-Algorithm
,	O
and	O
it	O
may	O
be	O
thought	O
as	O
the	O
union	O
of	O
four	O
copies	O
of	O
the	O
Hilbert	B-Algorithm
curves	I-Algorithm
combined	O
in	O
such	O
a	O
way	O
to	O
make	O
the	O
endpoints	O
coincide	O
.	O
</s>
<s>
Because	O
the	O
Moore	B-Algorithm
curve	I-Algorithm
is	O
plane-filling	O
,	O
its	O
Hausdorff	O
dimension	O
is	O
2	O
.	O
</s>
<s>
The	O
following	O
figure	O
shows	O
the	O
initial	O
stages	O
of	O
the	O
Moore	B-Algorithm
curve	I-Algorithm
:	O
</s>
<s>
The	O
Moore	B-Algorithm
curve	I-Algorithm
can	O
be	O
expressed	O
by	O
a	O
rewrite	O
system	O
(	O
L-system	B-Language
)	O
.	O
</s>
<s>
Here	O
,	O
F	O
means	O
"	O
draw	O
forward	O
"	O
,	O
−	O
means	O
"	O
turn	O
left	O
90°	O
"	O
,	O
and	O
+	O
means	O
"	O
turn	O
right	O
90°	O
"	O
(	O
see	O
turtle	B-Application
graphics	I-Application
)	O
.	O
</s>
<s>
There	O
is	O
an	O
elegant	O
generalization	O
of	O
the	O
Hilbert	B-Algorithm
curve	I-Algorithm
to	O
arbitrary	O
higher	O
dimensions	O
.	O
</s>
<s>
Traversing	O
the	O
polyhedron	O
vertices	O
of	O
an	O
n-dimensional	O
hypercube	O
in	O
Gray	B-Device
code	I-Device
order	O
produces	O
a	O
generator	O
for	O
the	O
n-dimensional	O
Hilbert	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
To	O
construct	O
the	O
order	O
N	O
Moore	B-Algorithm
curve	I-Algorithm
in	O
K	O
dimensions	O
,	O
you	O
place	O
2K	O
copies	O
of	O
the	O
order	O
N−1	O
K-dimensional	O
Hilbert	B-Algorithm
curve	I-Algorithm
at	O
each	O
corner	O
of	O
a	O
K-dimensional	O
hypercube	O
,	O
rotate	O
them	O
and	O
connect	O
them	O
by	O
line	O
segments	O
.	O
</s>
<s>
The	O
added	O
line	O
segments	O
follow	O
the	O
path	O
of	O
an	O
order	O
1	O
Hilbert	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
This	O
construction	O
even	O
works	O
for	O
the	O
order	O
1	O
Moore	B-Algorithm
curve	I-Algorithm
if	O
you	O
define	O
the	O
order	O
0	O
Hilbert	B-Algorithm
curve	I-Algorithm
to	O
be	O
a	O
geometric	O
point	O
.	O
</s>
<s>
It	O
then	O
follows	O
that	O
an	O
order	O
1	O
Moore	B-Algorithm
curve	I-Algorithm
is	O
the	O
same	O
as	O
an	O
order	O
1	O
Hilbert	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
To	O
construct	O
the	O
order	O
N	O
Moore	B-Algorithm
curve	I-Algorithm
in	O
three	O
dimensions	O
,	O
you	O
place	O
8	O
copies	O
of	O
the	O
order	O
N−1	O
3D	O
Hilbert	B-Algorithm
curve	I-Algorithm
at	O
the	O
corners	O
of	O
a	O
cube	O
,	O
rotate	O
them	O
and	O
connect	O
them	O
by	O
line	O
segments	O
.	O
</s>
