At first glance, your typical Cantor Set generation diagram can appear rather stilted & stodgy:

But what if there were a different way to envision this structure?  For example, what if we take that dull old line segment, flip it over (which doesn’t affect its numerical structure, of course), and bend it around in a circle, until its two ends meet, like so?:


Now that’s a little more interesting!


I’ve been calling this a “Cantor Angel” because, well, that’s what the shape looks like to me: some bizarre algorithmically-produced supernatural being in flight.

AND it has the advantage of magnifying (by projection around the circle’s center) each increasingly tiny section so that when you’re out in the 7th iteration it’s thicker across (due to expanded circumference) than it would be in the linear diagram, so it’s easier to see (and draw).  Thus, this circular layout helps us peek a bit further into the infinities hidden inside that single finite line segment!

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s