A God of Ordered Patterns

 For God is not the author of confusion.... 

1 Corinthians 14:33

"Scientists have made a groundbreaking discovery in quantum materials, revealing that electron energy levels in certain systems follow a fractal pattern known as Hofstadter’s butterfly.

A team of scientists at Princeton University has successfully

measured the energy levels of electrons in a new type of quantum material and discovered that they follow a fractal pattern, a repeating structure that looks the same at different scales. Fractals are commonly found in nature, in things like snowflakes, ferns, and coastlines. In the quantum world, a similar pattern called Hofstadter’s butterfly was theorized back in 1976. Now, for the first time, researchers have directly observed this pattern in a real material.

Hofstadter’s butterfly represents the principal finding of a seminal 1976 paper by Douglas Hofstadter. In this work, he predicted that the energy levels of electrons confined within two-dimensional crystals under the influence of a strong magnetic field would display a characteristic fractal energy spectrum. 

The “butterfly” moniker is used because the emerging pattern, when plotted against energy and magnetic field, evinces an elegant and intricate configuration that resembles a butterfly’s wings.

Importantly, this butterfly pattern is a fractal, meaning it is a self-repeating pattern that is produced over different scales, again and again. 

While there are many examples of fractals in nature—such as coastlines and snowflakes—few are found in the quantum realm.

“The Hofstadter’s regime is a rich and vibrant spectrum of topological states, and I think being able to image these states could be a very powerful way to understand their quantum properties,” said Michael Scheer, a graduate student in physics at Princeton and one of the paper’s co-lead authors." 

SciTechDaily