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 ...

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 ...

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 at the High ...

A bacterium has evolved an enzyme that assembles in a fractal structure, a mathematical pattern that repeats itself at smaller scales. Fractal patterns are found throughout nature on large, ...

By placing the cells on surfaces patterned with fractal shapes that mimic natural structures in the kidney, the team ...

Fractals are sometimes referred to as a “visual representation of math.” They can be observed in the spatial arrangements found in many familiar forms, patterns and shapes in nature: from the ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

A gallery of images spawned by the theories of the innovative mathematician, who died Oct. 14 at the age of 85 The Mandelbrot set, which is most commonly represented by the above illustration, ...

As Sigmund Freud made very clear, human beings are compelled to repeat patterns—the repetition compulsion. Patterns laid down early in life are propelled forward to recreate the familiar that can be ...