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Related Pages
Related Symbols
SierpinskiMesh
Area
Related Categories
Mathematics
The Area of a Sierpinski
Example Notebook
Open in Cloud
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Here is a 2-level Sierpinski mesh:
I
n
[
1
]
:
=
S
i
e
r
p
i
n
s
k
i
M
e
s
h
[
2
]
O
u
t
[
1
]
=
Generate meshes up to level 5:
I
n
[
2
]
:
=
T
a
b
l
e
[
S
i
e
r
p
i
n
s
k
i
M
e
s
h
[
n
]
,
{
n
,
5
}
]
O
u
t
[
2
]
=
,
,
,
,
Compute their areas:
I
n
[
3
]
:
=
A
r
e
a
/
@
%
O
u
t
[
3
]
=
{
0
.
3
2
4
7
6
,
0
.
2
4
3
5
7
,
0
.
1
8
2
6
7
7
,
0
.
1
3
7
0
0
8
,
0
.
1
0
2
7
5
6
}
The areas are linear on a log scale:
I
n
[
4
]
:
=
L
i
s
t
L
o
g
P
l
o
t
[
%
]
O
u
t
[
4
]
=
This continues to be true:
I
n
[
5
]
:
=
L
i
s
t
L
o
g
P
l
o
t
[
A
r
e
a
/
@
T
a
b
l
e
[
S
i
e
r
p
i
n
s
k
i
M
e
s
h
[
n
]
,
{
n
,
1
0
}
]
]
O
u
t
[
5
]
=
There is a linear fit to the log:
I
n
[
6
]
:
=
F
i
n
d
F
o
r
m
u
l
a
[
L
o
g
[
A
r
e
a
/
@
T
a
b
l
e
[
S
i
e
r
p
i
n
s
k
i
M
e
s
h
[
n
]
,
{
n
,
1
0
}
]
]
,
n
]
O
u
t
[
6
]
=
-
0
.
8
3
6
9
8
8
-
0
.
2
8
7
6
8
2
n
Related Symbols
SierpinskiMesh
Area
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