An archived instance of discourse for discussion in a Fractal Introductory Colloquium.

The Sierpinski carpet

mark

The Sierpinski carpet consists of 8 copes of itself scaled by the factor 1/3. It fits nicely into a square:

carpet.png600x600 99.3 KB

What is the Fractal dimension of the Sierpinski carpet?

Also, I generated that image using our IFS Visuzalizer. using the following IFS:

[
  scale(1/3),
  shift([1/3,0]).compose(scale(1/3)),
  shift([2/3,0]).compose(scale(1/3)),
  shift([0,1/3]).compose(scale(1/3)),
  shift([2/3,1/3]).compose(scale(1/3)),
  shift([0,2/3]).compose(scale(1/3)),
  shift([1/3,2/3]).compose(scale(1/3)),
  shift([2/3,2/3]).compose(scale(1/3))
]

Try it out! Do be careful with the deterministic mode, though. It can lock up your browser for a few seconds.