We finished our discussion of the first dimension calculation practice sheet with an observation that the S^d = N definition for dimension has some weaknesses, primarily:
- What do you do with fractals with non-iterating stems (e.g., 2 and 13)?
- What if the fractal is not exactly self-similar (like 5)?
- What if it is self-similar, but at differing scales (like 15)?
We will continue to work on our definition of dimension to accommodate these issues. You have also been issued a challenge: use what you’ve learned from the S^d=N definition to design a fractal with a dimension of exactly 1.5. Think about this as you read Gould’s essay Size and Shape.
We spent the rest of the period working on our FractaSketch designs.