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 ...

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot ...

Geometry in ecological patterns of landscape and vegetation is not truly fractal, and varies across a range of scales, whereas fractal geometry provides tools for predicting and describing ecological ...

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, ...

A new way of looking at cities that has emerged during the last 20 years that could revolutionize planning and ultimately benefit city dwellers. 'The Size, Scale and Shape of Cities' advocates an ...

Michael Rose does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

A new approach has given rise to the hope for a faster and more reliable method for determining cancer cell types. Scientists from the Max Planck Institute for Intelligent Systems in Stuttgart and the ...

We’re finding infinitely complex, self-similar shapes all over creation. And we’re just getting started. The world is full of beautiful geometry. It’s something we start teaching our youngest children ...