Block Fractals
Background - Area of the Gasket
Next we compute the area of the gasket by finding the area of families of squares that enclose the gasket ever more closely.
Level 1
Level 2
Level3
Level
Side Length
Number of Squares
Square Area
Total Area
1
1
1
1
1
2
1/2
3
(1/2)
2
=
1/4
3*(1/4) = 3/4
3
(1/2)
2
3
2
((1/2)
2
)
2
=
(1/4)
2
3
2
(1/4)
2
=
(3/4)
2
...
...
...
...
...
n
(1/2)
n-1
3
n-1
(1/2
n-1
)
2
=
(1/4)
n-1
3
n-1
*(1/4)
n-1
=
(3/4)
n-1
As n -> infinity, Total Area -> 0 and so
The gasket has zero area
Total Area vs level
Return to
Gasket perimeter and area
.
