When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$. ... read more >>

"New Directions in Numerical Computation" was a conference in celebration of Nick Trefethen's 60th birthday held August 25-28 in the new Andrew Wiles building, which houses the Mathematical Institute of the University of Oxford.... read more >>

A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its shortest axis, but not about its middle axis.... read more >>

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

My experience with the forthcoming MATLAB watch exceeds my most optimistic expectations. The watch has not yet been announced officially, but a few of us have been testing prototypes for the past several weeks.... read more >>

I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz.... read more >>

If $n$ is odd, replace $n$ by $3n+1$, if not, replace $n$ by $n/2$. Repeat. A famous conjecture made by Lothar Collatz is that no matter what value of $n$ is chosen to start, the process eventually terminates at $n=1$. Do not expect a proof, or a counterexample, in this blog. ... read more >>

The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March, 1964. ... read more >>

Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a seasonal holiday fractal that depends % upon the parameter phi. The default... read more >>

We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast finite Fourier transforms. This post, which describes touch-tone telephone dialing, is the first of three posts about the computation and interpretation of FFTs. The posts are adapted from chapter 8 of my book, Numerical Computing with MATLAB . ... read more >>