Math Help - fractal dimension of "filled" koch snowflake

1. fractal dimension of "filled" koch snowflake

The box counting dimension and Hausdorff dimension of Koch snowflake(shown below left) itself is log 4/log 3 ≈ 1.26.

I have a question: What about Koch snowflake with inside of it completely filled(shown below right)? Is the dimension 2? Or is it still log 4/log 3 ? Or something else?

I tried computational algorithm(box counting algorithm) to calculate the dimension numerically, and it gave dimension around ~1.83. I wonder where this number come from. Is it just a numerical error of the algorithm(where the answer should be 2)?

Thank you in advance for those reading this post.

2. This might be your answer [talks about "box (fractal) dimension"].

http://www.ncssm.edu/courses/math/TC...c_AllInOne.pdf

3. Wiki perspective

In most cases, there's no consistent definition for fractal dimension:

Fractal dimension - Wikipedia, the free encyclopedia