#mathematica

[daily-public-domain]

Day 364: "Broken glass 1"

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–This image is part of the public domain, meaning you can do anything you want with it! (you could even sell it as a shirt, poster or whatever, no need to credit it!)–

[as-if-and-only-if]

this whole time (over a decade???) I've been assuming that taking the length of lists in mathematica is an O(n) operation—when in reality the internal data structures implementing List store the length, making it O(1). As far as I can tell this is not officially documented anywhere. I just never tested it. Lol. Lmao, even!

[wikipediagrams]

[painfuldischarge]

MacRenderMan

Some historical floppy disk fun from old Pixar days. When Pixar decided to sell RenderMan to the public we had to come up with a good name (It was REYES, Renders Everything You’ve Ever Saw / Seen). You could already buy a version that a ran on the Pixar Image Computer CHAP (Channel Processor) called CHAPREYES. I don’t know if we ever sold any, but we did render Red’s Dream on it, in part. The…

[jadagul]

Working out how to do that polar video nicely helped me figure out how to do something I'd been working on for a while a couple years ago and never got where I wanted with: visualizations of elliptic curves as complex surfaces.

I went to see if I've talked about elliptic curves before, and I actually talked about this exact issue here. But now I've leveled up in Mathematica so I can do the visuals better.

Oversimplified, an elliptic curve is an equation that looks like y^2 = x^3+ax+b for some integers a and b. And they have lots of interesting number theoretic properties if you look for solutions that are rational numbers, none of which I want to talk about right now.

If you graph these equations over the real numbers you get pictures like one of these two (left: y^2=x^3+7x+1; right: y^2=x^3-7x+1):

And we like to imagine points at infinity in each direction, so the picture on the left looks like one giant circle (going through infinity at the top/bottom), and the picture on the right looks like two disconnected circles. And the difference is basically whether we get one or three solutions to the cubic when we set y equal to zero.

But over the complex numbers they should all look the same. The problem is, graphs of complex functions are four-dimensional and that's hard to display. But in that four-dimensional space, we should get a torus: a circle moved through a circular path (which still includes the point at infinity).

But we can make three-dimensional graphs, and then we can let them vary over time. So here is an animation of y^2=x^3+7x+1, with time controlling the imaginary coordinate of the output:

And here is y^2=x^3-7x+1:

You can see the moment in the middle where they "snap" into the real-plane-only version.

But now that I have these movies looking good, I want to go back and figure out better ways to slice them; here we're not getting "just" the "real solutions" plane ever, which I think makes them a little harder to interpret.

[nothoward]

Because.

- Newton's Fourth Law

[transmanray]

calculator for suicidal people

[allisongreenlee]

Ancient Civilizations: Euclid and the Legacy of Ancient Alexandrian Mathematics

The knowledge contained in Elements remained unmatched for centuries...

[saintdandy]

principia mathematica, russell

[peeterjoot]

Weighted geometric series

[Click here for a PDF version of this post] Karl needed to evaluate the sum: \begin{equation}\label{eqn:weightedGeometric:20} S = \sum_{k = 0}^9 \frac{a + b k}{\lr{ 1 + i }^k} \end{equation} He ended up using a spreadsheet, which was a quick and effective way to deal with the problem. I was curious about this sum, since he asked me how to sum it symbolically, and I didn’t know. Mathematica…

[daily-public-domain]

Day 257: When Claude met Vincent

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–These images are part of the public domain, meaning you can do anything you want with them! (you could even sell them as a shirt, poster or whatever, no need to credit them!)–

[contrasttrim]

mi estúpido chud hijo

[wikipediagrams]

[dd3ah]

Mit dem Raspberry Pi arbeiten viele Funkamateure. Hier wird beschrieben wie man das mitgelieferte Wolfram Mathematica nutzen kann um ein besseres Verständnis zu erhalten, was bei Frequenzmodulation geschieht.

[bar-apps]

Matlab o Mathematica

¡Descubre las diferencias entre Matlab y Mathematica de Wolfram en el ámbito técnico y científico! En esta página, explorarás las distintas aplicaciones de estas potentes herramientas en áreas como matemáticas, procesamiento de señales e imágenes