27
Mar
08

Weierstrass Function

The infamous Weierstrass function is an example of a function that is continuous but completely undifferentiable. \displaystyle \sum_{k=1}^{ \infty}\frac{sin(\pi{k }^{a}x)}{\pi{k}^{a}}

(* runtime: 0.7 second *)
Plot3D[Sum[Sin[Pi k^a x]/(Pi k^a), {k, 1, 50}], {x, 0, 1}, {a, 2, 3}, PlotPoints -> 100];

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8 Responses to “Weierstrass Function”


  1. 1 _ex_
    May 6, 2008 at 3:02 am

    your blog is incredible! 😀

  2. 2 edi15ta
    May 11, 2008 at 5:04 pm

    Great blog! What machine do you have?! For my Mathematica it took about 3 minutes… (Intel C2D 2,16GHz, 2.5GB RAM). I guess the MathGL3D gives you the speed up, am right?

  3. 3 nylander
    May 12, 2008 at 1:37 am

    I don’t know why it takes longer to run on your machine. I am using Mathematica 4.2 on a laptop with AMD Dual-Core, 2 GHz 512 K processor and 1GB memory, and it takes about 0.7 second. It used to be a little bit slower on my previous laptop, but not much slower:

    Plot3D[Sum[Sin[Pi k^a x]/(Pi k^a), {k, 1, 50}], {x, 0, 1}, {a, 2, 3}, PlotPoints -> 100]

  4. 4 ma65p2004
    June 8, 2008 at 6:46 am

    Uhm, I have no idea what you are talking about in your posts. You got pretty pictures though. (:D). I’m going to be an chemical engineer, so i guess this is what engineers do. It looks funnn!!! (even though I don’t understand any of it.) Too bad you don’t have an about page. I can’t keep reading, my brain will explode. But I’m subscribing.

  5. June 19, 2008 at 2:51 am

    Somehow i missed the point. Probably lost in translation 🙂 Anyway … nice blog to visit.

    cheers, Senescence.

  6. July 11, 2008 at 10:49 am

    Mm very impressive math animations! I’m interested in fractal animations now, and all stuff in your blog are kind of it. Thanx for all infos, all the best 🙂

  7. 7 Steven
    July 15, 2008 at 3:15 pm

    Just surfed in. Great blog Paul, a pleasure to have viewed it.

  8. November 14, 2008 at 9:21 am

    VERY NICE BLOG!!!!
    i will recommend it to many of my friends 😀


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