A few months ago, I had never heard of Karl Menger or the cube-like fractal that he invented. Now I have this long blog post about the sponge, and an extension that I am calling its "associate".... 더 읽어보기 >>

A cube is the familiar three-dimensional solid with eight vertices, six faces and twelve edges. I have been working with cubes recently in posts about both the Menger sponge fractal and the 4-by-4 matrix from computer graphics.... 더 읽어보기 >>

The complement of an evolving Menger sponge is all of the material that has been removed so far.... 더 읽어보기 >>

Season's Greetings 2021 __________________________________________________________Marc Lätzel (2021). XMas Tree (https://www.mathworks.com/matlabcentral/fileexchange/9337-xmas-tree),MATLAB... 더 읽어보기 >>

On a recent visit to Ann Arbor, I met ten-year old Eden Rajapakse. Here is her sketch of the L-shaped membrane. Download Live... 더 읽어보기 >>

The Menger sponge is a popular fractal that generalizes Cantor sets and Sierpinski triangles. Its fractal dimension is between two and three.... 더 읽어보기 >>

Matrices in action.... 더 읽어보기 >>

See Cube and Teapot.... 더 읽어보기 >>

Use a cube instead of the Utah Teapot in my previous post. I was pleasantly suprised by the final screen shot.... 더 읽어보기 >>

Matrices like the ones shown in the following screen shots are at the heart of computer graphics. They describe objects moving in three-dimensional space. MATLAB's Handle Graphics uses them. So does MathWork's new RoadRunner editor. And so do all popular video games and CAD packages.... 더 읽어보기 >>