The answer is that fractals have a tendency to repeat at different scales. This is called self-affine and self-similar but it means a weekly pattern will look very like the daily, the hourly ...

The novelty (and surprise) is that these self-affine fractal curves exhibit a wealth of structure—a foundation of both fractal geometry and the theory of chaos. A few selected generators yield ...

Self-affine tiles and fractal geometry form a rich field where geometric precision meets the complexity of nature’s form. At its core, the subject examines how self-affine tiles—constructed ...

Spectral measures and self-affine fractals represent a thriving intersection between harmonic analysis and fractal geometry. In essence, a spectral measure is defined as a measure for which the ...

The affine-similar fractal is a bit different than your standard self-similar fractal. While it technically features pattern repetition, you won’t need to zoom in to see it. Rather, the ...

This program will draw fractals with an Iterated Function System or by the Chaos Game. Either method requires that the transformations defining the IFS be given. An IFS is composed of a number of ...

Fractal geometry is one of the most elegant and beautiful branches of mathematics. An early analysis of fractals came from a surprising and weird phenomenon that occurs when you try to measure a ...

You may not be able to define “fractal” — yet — but fractals are, in fact, everywhere. As you might expect from hearing her title, Hayley Brazier, Donald M. Kerr curator of natural history ...