I decided to postpone our discussion of Gould’s essay, assigned on Friday, so that we could finish our discussion of the first dimension calculation practice sheet, which we did so with an observation that the S^d = N definition for dimension has some weaknesses. In particular:
- 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.
We spent the rest of the period working on our FractaSketch designs.