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Showing posts from January, 2016

Cardiod in a Cup

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Cardiod in a Cup

Sarah Nemec-Nelson and I were having dinner over the holidays, and I was surprised to see this shape when I glanced at my coffee cup.  It's a cardiod!  In this case, it was the result of distant light reflecting off the conically shaped mug.

Relevant Links

Wikipedia:
https://en.wikipedia.org/wiki/Cardioid
https://en.wikipedia.org/wiki/Caustic_(optics)
https://en.wikipedia.org/wiki/Caustic_(mathematics)

Rolling Circles and Balls, a nice series by John Baez
https://johncarlosbaez.wordpress.com/2012/08/31/rolling-circles-and-balls-part-1/

Travel to the past

Travel to the past

This is truly mind-bendingly fantastic.  If you watch it a few times, you'll start noticing all sorts of subtle details.  My mind hasn't been able to resolve the paradoxes it evokes.

Originally shared by Henry Segerman

In Which the Viewer Time-Travels into the Past by the Use of Portals: A Spherical Droste Video.
https://www.youtube.com/watch?v=qvh-EAipIUk

{3,6,∞} honeycomb in spherical video

{3,6,∞} honeycomb in spherical video

...and now spherical video of a honeycomb with a repeating euclidean pattern on the upper half space boundary.  To get the animation this time, a parabolic Möbius transformation with a fixed point at the south pole is applied, an idea suggested by Henry Segerman.

I slowed the movement down a bit and made it longer.  The colors don't change under this transformation because we aren't moving through different cells.  

Again, you should be able to extend the playback even more by right-clicking and selecting "Loop".
https://www.youtube.com/watch?v=wjeeMlHsYjE&feature=share

Spherical video moving through a hyperideal honeycomb

Spherical video moving through a hyperideal honeycomb

Inspired by Henry Segerman's recent spherical video and blog post (plus.google.com/+HenrySegerman/posts/YYkNxjrpMmW), I decided to experiment with doing a spherical video of one of our hyperideal honeycombs.  This is the first result, using the {4,3,7} honeycomb.  

We are inside the honeycomb, zooming towards the south pole of the visual sphere and away from the north pole. Trippy!  I wish it was a bit longer, but this definitely whets my appetite to try more.

update: it's not a perfect repeat color-wise, but you can right-click the video and select "Loop" for a more extended experience.

See hyperbolichoneycombs.org for more info.
https://www.youtube.com/watch?v=51ow3XAjG6Y&feature=share