There on Donald Davis’s computer screen, little dots are growing into lines, and the lines are growing into swirls, and the swirls, Davis promises, will soon grow into a snake – all planned out by the ...

Even the smallest taste of a fractal is guaranteed to blow one’s mind, wrapping up psychedelic satisfaction and hardcore mathematics in a bite-sized (er, infinite-sized?) package. Tom Beddard, a laser ...

In a mesmerising blend of art and mathematics, a research student from University College London (UCL) has recently gained widespread attention for creating intricate images solely through ...

In mathematics, simple equations can generate a complex evolution in time and intriguing patterns in space. One famous example of this is the Mandelbrot set, named after the French-American ...

What makes a tree a tree? Or rather, why can we recognize trees in even quite abstract depictions when they are so varied in nature? Researchers have found a clue in the branches, and used math to ...

One of the first studies of fractals came from a surprising and weird phenomenon that occurs when you try to measure a coastline.

Fifty years ago, “fractal” was born. In a 1975 book, the Polish-French-American mathematician Benoit B. Mandelbrot coined the term to describe a family of rough, fragmented shapes that fall outside ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...