Fractal geometry investigates complex shapes that exhibit self-similarity across multiple scales, while spectral analysis focuses on the study of the eigenvalues and eigenfunctions of operators, most ...

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 ...

Fractal geometry is a field of math born in the 1970s and mainly developed by Benoit Mandelbrot. If you’ve already heard of fractals, you’ve probably seen the picture above. It’s called the Mandelbrot ...

Though now extinct, ammonoids (a group of marine mollusks with shells) evolved for 350 million years, always with a tendency toward increasingly elaborate shell structures. Scientists have studied ...

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 ...

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, ...

Drawn from the irregular shapes and processes found in nature, his research benefited a wide array of fields, from art to physics and finance. Steven Musil is a senior news editor at CNET News. He's ...

We live in a world of three-dimensional objects bounded by two-dimensional surfaces and outlined by one-dimensional lines. All in all, a comforting, intelligible, whole-number sort of world. Or do we?