How many dimensions?

A number of the things I’ve been showing here recently come in two flavors — two dimensional and three dimensional. For example, I first showed the springy ball/stick model in two dimensions, and then quickly moved it to three dimensions (which seemed to make it richer).

I wonder what effect this would have on other things, like fractal Koch snowflakes, or musical candy button machines. It’s not clear that everything would benefit from that third dimension. Certain things might actually have a natural affinity for two. In those cases, adding depth might break some important symmetry, or only add confusion.

It seems like an interesting way to think about any particular thing: Some things might really want to live in only one dimension — others really require four or even more (which can be really problematic if you’re trying to look at them). It seems like a useful question to ask, whether you are talking about music or a snowflake: For any given object or idea, how many dimensions does it want to have?

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