Block Fractals

Sample

Although we build the stages of the models with blocks of the same size, for these calculations we rescale successive stages by a factor of 1/2.

Count the number of cubes at each level.

At each level, calculate the perimeter of the cubes, the areas of the cubes, and the volumes of the cubes.

Look for patterns in the perimeters, areas, and volumes.

Use this information to find the perimeter, area, and volume of the limiting shape.

How does the dimension of the limiting shape explain these results?

Level 1	Level 2	Level 3

Level	Side Length	Number of Cubes
1	1	3
2	1/2	32
3	1/4	33
n	1/2n	3n+1

Here we calculate the perimeter of the stages, and take the limit.

Here we calculate the area of the stages, and take the limit.

Here we calculate the volume of the stages, and take the limit.

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