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 ...

Computer simulations of electrical charges sent to retinal implants based on fractal geometry have researchers moving forward with their eyes focused on biological testing. Computer simulations of ...

HOW do you spot a fit partridge? Check out the fractals round its neck. Fractal geometry is used when a pattern is too complex to be described by Euclidean geometry. It has been applied to coastlines, ...

"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 ...

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 ...

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 ...

What do coastlines, clouds, cauliflower and the stock market have in common? Mathematician Benoit Mandelbrot may not have conceived the question, but he provided an answer — one that was compelling in ...

Benoit Mandelbrot, the Polish-born, French and American mathematician, known as the "father of fractal geometry," is celebrated in today's Google Doodle, on what would have been his 96th birthday.