#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!)–

[shonk]

⌗

[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

[mathart]

Vertex normals in a Mathematica Manipulate[]

This is not obvious or easy in Mathematica, because Import[... , "OBJ"] does not preserve Winged-Edge mesh topology. So, you have to go through considerable effort to associate doubly-connected mesh edges back to polygons to compute the equivalent normal vector to the surface located at the vertices.

[allisongreenlee]

Ancient Civilizations: Euclid and the Legacy of Ancient Alexandrian Mathematics

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

[dark-white1]

Hello friends. I uploaded my first application to the Google Play store. Can you download it to help me even if it is an amateur game.

[daily-public-domain]

Day 247: Riemann Zeta landscape

link

–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!)–

[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

[albeo]

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