Comments for The Math Less Traveled

Comment on Workshop on Functional Art, Music, Modeling and Design by Konstantinos

Konstantinos — Tue, 14 May 2013 12:43:16 +0000

Sounds very cool! Thanks for sharing!

Comment on Making connections by romain

romain — Fri, 03 May 2013 12:44:51 +0000

That’s a very interesting subject! I coded it and started to play with it: there are many phenomena worth studying. For example, the total number of lines seems to peak at the 55th neighbour with more than 99 lines. For comparison, it only reaches 69 in the first neighbour case. I guess this could be derived rigorously by computing the probability that two nodes are mutually their kth nearest-neighbour.
It would be worth computing the modularity of the graphs or other such measures…

However, when you reach the 99-100th nearest-neighbour, the 4 angles attract pretty much all the lines. A version avoiding this would consist in taking a uniform circle for the positions of dots.

Comment on Making connections by Shaun

Shaun — Sun, 28 Apr 2013 00:59:12 +0000

I will admit that I had absolutely no idea about your reasoning for building the connections that you did, but after reading the comments above, I finally get it.

Comment on Animated Sieve of Eratosthenes by Per Persson

Per Persson — Fri, 26 Apr 2013 15:21:22 +0000

It should say .

Comment on Animated Sieve of Eratosthenes by Per Persson

Per Persson — Fri, 26 Apr 2013 15:18:58 +0000

Of course… For large we will have and taking will compensate for those factors.
Have you studied what the limit function will look like?

Comment on Making connections by Brent

Brent — Mon, 22 Apr 2013 01:31:54 +0000

Something like that. I don’t remember the exact numbers I used. Note, however, that the final one corresponds to the 100th closest (or maybe 95th, something close to that anyway)—all the edges go diagonally to the furthest corner.

Comment on Making connections by Brent

Brent — Mon, 22 Apr 2013 00:13:29 +0000

Cool, didn’t know that!

Comment on Making connections by Devin

Devin — Sun, 21 Apr 2013 21:13:41 +0000

[squint] Perhaps the second row isn’t 5th-closest neighbor? Maybe the 11th closest? In which case the next rows are 21st and 31st? Great fun!

Comment on Making connections by td

td — Sun, 21 Apr 2013 04:23:34 +0000

In effects for movies, these connection tricks are used all the time. For instance in particle simulations points will move around based on some dynamics and then turned into a volume by connecting n-closest with segments. It’s sometimes easier to design the effect and visualize the end result than moving around volumes. plenty of examples here: http://www.imdb.com/video/imdb/vi3445005593/
not a great movie though.

Comment on Making connections by Brent

Brent — Sat, 20 Apr 2013 18:32:00 +0000

Right! The only thing that’s not quite accurate is Devin’s comment “Same for the nth group in the grid (L-to-R, T-to-B).” Look more carefully… =)

This was fun for me since I actually had no very good idea of how it would look before I tried it. It’s interesting that with connecting nearest neighbors you end up with lots of small connected structures. I wonder — what is the expected number of points in one of those connected structures?