My Favorite MATLAB Demos - Cleve Moler on Mathematics and Computing
 

In 1988, while I was with Ardent Computer in Silicon Valley, I gave a talk that previewed MATLAB graphics. The title was "Pictures of Matrices". At the time, a mathematician friend of mine asked.

Why would anyone want pictures of matrices?My response is the graphics demonstrations that we have done over the years. Here is a baker's dozen of my favorite examples.

[B]Contents[/B]
[LIST][*][URL="#1050b54b-03cc-4651-a92f-08b47bce1aba"]Vibes[/URL][*][URL="#cca646f4-d29d-4f64-8b12-9c8d6868aa07"]Pitch, Roll and Yaw[/URL][*][URL="#523be0a1-ef64-4117-8827-aadab1aec717"]Rubiks Cube[/URL][*][URL="#6c148e13-491e-48c4-8a1f-17bd6e1208ab"]Eigenwalker[/URL][*][URL="#5808e6ab-e3fa-4128-b43b-94218f7d6659"]Simulation[/URL][*][URL="#37dae5b7-d02a-41e0-805c-11d11d1418f8"]Sponge[/URL][*][URL="#9916dfbf-68eb-45a6-8e75-695014dcbc68"]Drums[/URL][*][URL="#744ce13d-9dbe-42d9-a2df-f3d6dc3c2548"]Jahnke and Emde[/URL][*][URL="#52de6435-9b73-4c4e-8402-401b64ad6571"]Penny[/URL][*][URL="#3fe4f412-05a9-4faf-823f-321a39baeb80"]Jordan Form[/URL][*][URL="#c90e69f0-d3f5-4e44-a23a-c7434bffc251"]Expshow[/URL][*][URL="#b73f8b6f-ac84-4b66-9b08-303afb8eaf13"]Eigshow[/URL][*][URL="#8cac3156-b0b3-47d7-abf4-653302fc719c"]Eden[/URL][/LIST][B]Vibes[/B]

The vibrating L-shaped membrane.

[URL]https://blogs.mathworks.com/cleve/2023/12/13/blog-post-number-300-vibrating-logo/[/URL].

[IMG]http://blogs.mathworks.com/cleve/files/vibes.gif[/IMG]

[B]Pitch, Roll and Yaw[/B]

Studying rotations.

[URL]https://blogs.mathworks.com/cleve/2023/02/10/grafix-users-guide/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/Graphics.png[/IMG]

[B]Rubiks Cube[/B]

The world's greatest mathematical puzzle.

[URL]https://blogs.mathworks.com/cleve/2022/04/04/digital-simulation-of-rubiks-cube/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/Qube_simplified.png[/IMG]

[B]Eigenwalker[/B]

Principle component analysis of the human gait.

[URL]https://blogs.mathworks.com/cleve/2016/04/11/the-eigenwalker-model-of-the-human-gait/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/walker.gif[/IMG]

[B]Simulation[/B]

Simulink at the test track.

[URL]https://blogs.mathworks.com/cleve/2023/09/11/exploring-matrices/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/Simulink.png[/IMG]

[B]Sponge[/B]

The Menger sponge is a popular fractal that generalizes Cantor sets and Sierpinski triangles.

[URL]https://blogs.mathworks.com/cleve/2021/12/06/the-menger-sponge-fractal/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/sponge2.png[/IMG]

[B]Drums[/B]

Contour plots of isospectral pairs.

[URL]https://blogs.mathworks.com/cleve/2012/08/06/can-one-hear-the-shape-of-a-drum-part-1-eigenvalues/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/drums.png[/IMG]

[B]Jahnke and Emde[/B]

Contour plot of the Hankel function, based on a hand drawing in a 1933 book by German mathematicians Eugene Jahnke and Fritz Emde.

[URL]https://blogs.mathworks.com/cleve/2014/12/15/jahnke-and-emde-revisited/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/jahnke.png[/IMG]

[B]Penny[/B]

High resolution measurements of the depth of the mold for the United States one cent coin.

[URL]https://blogs.mathworks.com/cleve/2014/03/17/higher-resolution-penny/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/penny.png[/IMG]

[B]Jordan Form[/B]

Jordan Canonical Form of the 64-by-64 Redheffer matrix from the [URL="https://www.mathworks.com/help/releases/R2024b/matlab/ref/gallery.html"]MATLAB Gallery[/URL].

[URL]https://blogs.mathworks.com/cleve/2025/06/12/a-million-dollar-matrix/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/jcf64.png[/IMG]

[B]Expshow[/B]

An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in mathematics.

[URL]https://blogs.mathworks.com/cleve/2015/07/27/discover-e-with-a-graphical-experiment/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/expshow.gif[/IMG]

[B]Eigshow[/B]

One of my all-time favorite MATLAB examples is eigshow.

[URL]https://blogs.mathworks.com/cleve/2013/07/08/eigshow-week-1[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/eigshowp.gif[/IMG]

[B]Eden[/B]

This sketch of the MathWorks Logo was made by Eden Rajapakse when she was ten years old. Her blog post has received more "likes" than any other post.

[URL]https://blogs.mathworks.com/cleve/2021/12/23/a-new-view-of-our-logo/[/URL]

[IMG]http://blogs.mathworks.com/cleve/files/Eden.png[/IMG]

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