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.
$ 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
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.
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.
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. :)
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.
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[ 0.21 ms ] story [ 21.5 ms ] threadhttp://asymptote.sourceforge.net/gallery/animations/
http://www.piprime.fr/developpeur/asymptote/animation-asy_as...
http://www.marris.org/asymptote/animations/index.html
I also recommend http://blog.matthen.com/ (tons of math gifs with source code) and http://visualizingmath.tumblr.com/ (lots of gifs and other images along these lines).
Dynamical Systems and Fractals (http://www.amazon.co.uk/Dynamical-Systems-Fractals-Computer-...)
Mathographics (http://www.amazon.co.uk/Mathographics-Robert-Dixon/dp/048626...)
Computers Pattern Chaos & Beauty (http://www.amazon.co.uk/Computers-Pattern-Beauty-Clifford-Pi...)
Fractals Images of Chaos (http://www.amazon.co.uk/Fractals-Images-Chaos-Penguin-Scienc...)
I suggest these because they all contain some kind of code.
http://dvdp.tumblr.com/ artsy
http://i.imgur.com/gUm1T5S.gif
http://i.imgur.com/xR5uqle.gif
http://i.imgur.com/SVvuRII.gif
[1]: http://www.pheelicks.com/2013/10/intro-to-images-in-go-part-...
That's why math is fun. You can always participate in the analysis.
http://i.imgur.com/fxHj3kZ.gif
http://giphy.com/tags/geometry/
http://giphy.com/tags/math/
http://giphy.com/tags/physics/
[1] http://beautyandthemaths.tumblr.com/post/62281036101/the-ave...
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.
I know it might seem a little facile but a nice plot like that would look pretty cool on my website. :)