☞ Some Measured Fractal Dimensions

Fractals are great. I assume most readers are aware of these shapes, but very roughly (oy!), they are shapes that, due to their self-similarity and “crinkliness,” have dimensions that can be thought of as fractional. A fractal might effectively be somewhere between a line and a surface because it is a line that can fill an entire space (so its dimension is between 1 and 2), or its dimension might be between a surface and a solid shape, so between 2 and 3, for instance. This sounds weird and counter-intuitive and I am likely not even close to doing this concept justice, but it can be calculated. For example, the Sierpiński triangle has a dimension of about 1.585 (as per Wikipedia):

But the fractal dimensions of real world shapes can also be estimated. Which is why I really enjoy the fact that there is a Wikipedia page entitled “List of fractals by Hausdorff dimension” (a measurement of this fractal nature). And in it are found the following delights:

• Coastline of Ireland: 1.20 ± 0.01

• Coastline of Great Britain: 1.25

• Coastline of Norway: 1.52

• Balls of crumpled paper: 2.5

• Surface of human brain: ~2.8

• Lung surface: 2.97

Good job evolution on developing lungs that have a surface that are almost effectively a fully three-dimensional object!

Check out the entire list. ■

You might wish to check out my new Microcosm Industries newsletter:

From the Wikipedia page on the Little Professor, a “backwards-functioning calculator designed for children ages 5 to 9”:

The second generation Little Professor was designed by Mark Bailey, now a full life-sized professor…

Fantastic.

Here are some links worth checking out that touch on the complex systems of our world (both built and natural):

🜸 Idea Injection: “It may not be possible to have both immediate currency — quotability — and long-term significance. You might have to choose between Smith’s model and Keynes’s.” Cf. my “Constructing Signposts in the Memescape”

🝤 Factories are just rooms: “I want to re-home manufacturing. I want these kids to become designers, engineers, inventors, factory owners, and all the rest. Makers of any kind; participants in the ongoing making of our world.”

🜸 Latent Space as a New Medium

🜚 What Big Food Did to Ice Cream: ‘The “encrapification” of the American pint — a chemist’s plain-language dissection’

🝳 Obfuscated, self-evaluating bash script by CDN Akamai being supplied to consumers via retail stores

🜚 How Japan’s railways stayed one while splitting apart

🝤 How a Second-Grade Teacher Revived a Beloved Video Game: “Backyard Baseball, a favorite game for 1990s kids, had been off the market for years. But Lindsay Barnett was determined.”

Until next time.