Block Fractals

Exercises - Four Block Configuration Interpretation

We have seen the limiting shape has dimension Log(4)/Log(2) = 2..

Because the dimension lies between 1 and 3, we expect

the 1-dimensional measure is infinite and

the 3-dimensional measure is zero.

Indeed, our computations agree with this.

The perimeter is infinite.

The volume is zero.

Being a 2-dimensional measure, the area is more delicate to determine. Our calculations show the area is bounded above by 4.

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