$ curl -s http://4.bp.blogspot.com/-MPv_CwvvwKQ/Ulrw3TfdgyI/AAAAAAAAAEw/YsRPmU6C5xM/s1600/trefoil_rotate_white.gif |strings|grep -i created
UCreated by Wolfram Mathematica 9.0 for Students - Personal Use Only : www.wolfram.com
When I opened the first page I thought that it would be a page of unrelated GIFs. I saw the first one, read the accompanying paragraph, and stopped to think about it. I thought for a while before proceeding on, at which point I noticed that I had just thought through the next several GIFs of explanation.
That's why math is fun. You can always participate in the analysis.
This was exactly how I made sprite animations back in my Amiga demo coding days.
Take a look at early C64/Amiga demos and you'll recognize these patters.
These are really neat, but one thing I don't understand is the animation they linked to (i.e. the post that inspired the OP) [1]. Unlike the animations in mathgifs, my brain isn't interpreting anything there as rotational motion. Am I missing something?
That was the same with me. I guess it is because the dots are already colored, thus leading one's focus towards the translation. However if you ignore the colors and imagine a 3-petal flower, then you can see the flowers rotate counter-clockwise. Try following the outer edges where the density of dots is sparse and less confusing to form a mental image of the petal.
The dots are further spaced apart so so your eyes are drawn towards individual balls rather than the image as a whole. Plus as the balls are already coloured and you have ball tails, it's easier to see the ball paths.
Also, worth mentioning is the balls on this follow a subtly different path as they don't intersect the centre of the shape like they do in the article's gif.
Excellent! I'll have to spend a while exploring the archives. I just happened to have "proved" to myself the linearity of a very similar animation a few weeks ago. :)
Interesting, but I still have a headache since I looked at the gifs about an hour ago. Maybe it's just me but I would advice putting a warning somewhere.
