A mathematician has developed a new way to uncover simple patterns that might underlie apparently complex systems, such as clouds, cracks in materials or the movement of the stockmarket. The method, ...

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 ...

Fractal patterns that arise when healthy human cells turn cancerous have been observed for the first time by scientists in the US. Using an atomic force microscope (AFM), Igor Sokolov and colleagues ...

When it comes to the study of both human nature and the natural world, one must be willing to reckon with the fact that a certain degree of chaos will be present in whatever facets of this planet they ...

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 via affine ...

There are multiple examples of fractal patterns in nature, from peacock feathers, snowflakes, and leaves, to cloud formations and coastlines. A group of graduate students have spotted similar fractal ...

Fractal geometry has emerged as a powerful analytical framework in geographic analysis, offering new ways to understand the inherent complexity and self‐similarity of urban forms. By focusing on ...