Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.)

Can you figure out what’s going on? The source code for the animation is here; I was inspired by Jason Davies’ visualization which was in turn inspired by this.

Reblogged this on nebusresearch and commented:

The Math Less Traveledhas a lovely video here, animating the Sieve of Eratosthenes, one of the classic methods of finding all of the prime numbers one wants. I suppose it won’t eliminate writing out and crossing off numbers for extra credit on a math test. I actually remember that being one test I had in, I believe, seventh grade, for reasons that I don’t think I ever got. Possibly the teacher wanted to have an easy time grading, or was giving everyone a break from too much computation by shifting to evaluation of our crossing-out abilities.Brent -

Could you take a look at “Sloppy Computing” and give your opinion ? Specifically, does this form of computing dramatically increase computer power for math programs (Like simulators) ?

Yes, I think “sloppy computing” is a very cool idea. Ultimately, I think it’s primarily more about reducing power usage than it is about increasing speed — as computers get smaller, power consumption and heat dissipation are becoming major limiting factors. Sloppy computing could indeed be very useful for certain types of computations such as simulation.

I love it. Gorgeous, and gives a lot of feel for the sieve.

Is there anyway to add a counter in the lower left – to show what number you’re at?

Oh, a counter in the lower left is a good idea!

This gave me the idea to form the infinite product . The primes will be those integer where .

The infinite product you give converges to zero for every value of x so f(x) = 0 identically.

So f’(x) = 0 identically.

Thanks, I actually suspected that. Can you find a way to account for this by for example defining a sequence of functions and setting so that the sequence converges?

Cn = (n!)/(pi^(n-1) x^(n-1)) .

Of course… For large we will have and taking will compensate for those factors.

Have you studied what the limit function will look like?

It should say .

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