Like Moths to a Flame (Help?)
Every teacher has a muse. Sometimes it’s clear that you’ve stumbled upon something that’s going to be the best lesson ever, and sometimes you bumble into something and all you get is that feeling like when you’re sleeping and the airplane drops 20 feet unannounced.
In short: help. Where’s the math here? What’s the lesson? I just can’t quit cull this one out.
Lifted from National Geographic. Moths.
and two:
The Cornally family fire pit.
Timon Piccini:
August 26th, 2012 at 3:04 pm
I assume there’s something in there about Chaos Theory. I instantly want to do a compare and contrast. I notice a lot more “loop-de-loops” in the moth picture whereas the fire looks more random. Why is that?
I want to look into flight patterns of a single moth, and then see if I can write a program that mimics the picture.
I want to talk about why fire was such a difficult process for CGI animators to make it look believable.
I dunno those are my thoughts right now.
Andy Rundquist (@arundquist):
August 26th, 2012 at 4:24 pm
The fire sparks follow thermal currents (and, of course, add to them). Moths follow scent trails (if I recall correctly). They, too, follow thermal currents, right?
Hillby:
August 26th, 2012 at 5:23 pm
I’m thinking density functions. Like probability that a moth or ember will be within a certain distance of the center of the light or flame at a given moment. You could probably compress the image and compare brightness levels.
jsb16:
August 26th, 2012 at 7:57 pm
The moths look like pictures from cloud chambers ( http://www.universetoday.com/58521/cloud-chamber/ ), where the paths are dictated by a (magnetic) force that depends on the particle’s velocity…
Evan:
August 26th, 2012 at 8:46 pm
I heard that moths’ brains are designed to try to keep a constant angle with respect to the plane of polarization of sunlight. Since light rays from the sun are basically parallel to one another on Earth, this enables moths to fly in a straight line. A light bulb, however, emits light rays in a radial pattern. So as a moth flies through light from a light bulb, the moth’s tendency to want to maintain a constant angle with respect to the polarization of the light will actually cause it to spiral.
I don’t know if that helps, but maybe it can inspire something. Vector curl or divergence?
Julia:
August 27th, 2012 at 1:19 am
Could lead to a discussion and modeling of different alternative explanations. I thought first of random walk/brownian motion (with fixed end points) which shouldn’t be to difficult to program into an appropriate software or even a calculator, to see whether the model looks right. Discussion: deterministic/random processes, chaos (this isn’t chaos through), attracting limit cycles… Most of this needs higher math than your average hs student possesses, but maybe you could work around that small difficulty.
Shawn:
August 27th, 2012 at 5:09 pm
Programming! OMG! Why didn’t I think of that. I’m going to make a sandbox for my kids to play in using Processing.
Shawn:
August 27th, 2012 at 5:12 pm
My brain immediately went “div! grad! curl!” I’ve read about the polarization thing in geese. I didn’t know there was evidence for it in insects, but I’m going to use this to motivate derivatives of trig functions in class. Thanks! I wonder if catching some moths and then playing with some polarized sunglasses would be in order? (Yes)
Alexandre Owen Muñiz:
August 30th, 2012 at 1:35 pm
A 2D analog is worm trails. Making a credible worm path is a good programming problem; I took it up as a personal challenge on my graphing calculator when I was in high school. There are some good connections to trig, randomness, and derivatives. (What exactly is the quantity you want to have vary randomly to make a credible worm path?) I had a real epiphany when I figured out a term that would be helpful as an adjustment to the change in curvature. It was the first time that I can recall picking a function not because of some justification from an authority, but because it was what worked for a design purpose. There was a serious feeling of freedom when I realized you could just do that!
Shawn:
September 4th, 2012 at 8:02 pm
Do you have a link for worm trails? Is it like the game snake?