# Rotation Matrices3

The matrices in the following animations are at the heart of computer graphics. They describe objects moving in three-dimensional space and are essential to MATLAB's Handle Graphics, to Computer Added Design packages, to Computer Graphics Imagery in films, and to most popular video games. Many modern computers contain GPUs, Graphic Processing Units, which are optimized to compute the product of these matrices.... 続きを読む >>

# Digital Simulation of Rubik’s Cube with Qube2

This blog post describes Qube, my Rubik's Cube simulator. Source code for Qube is now available in one single file from this link: Qube_osf.m. I will also submit the code to the MATLAB Central File Exchange. As usual, I welcome any feedback.... 続きを読む >>

# Digital Simulation of Rubik’s Cube1

Rubik's Cube is one of the great mathematical puzzles of all time. Most people are just interested in solving Rubik's Cube rapidly, but deeper investigation reveals a rich mathematical and computational structure. A digital Rubik's Cube simulator provides a laboratory for the study of linear algebra, group theory, data structures and computer graphics.... 続きを読む >>

# The Enigma Qube, Merging an Enigma Machine and a Rubik’s Cube2

An Enigma Machine combined with a Rubik's Cube makes an encryption device with unprecedented power.... 続きを読む >>

# What is A\A?

The answer: A\A is always I, except when it isn't.... 続きを読む >>

# Rubik’s Cube2

My recent obsession with cubes in this blog has led me back to Rubik's cube, perhaps the greatest mathematical puzzle of all time.... 続きを読む >>

# The Menger Sponge, Complement and Associate2

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".... 続きを読む >>

# Anatomy of a Cube3

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.... 続きを読む >>