Are fractals quantum?

Now physicists at MIT and elsewhere have for the first time discovered fractal-like patterns in a quantum material — a material that exhibits strange electronic or magnetic behavior, as a result of quantum, atomic-scale effects.

How are fractals used in physics?

Fractal structures arise in geophysics, in maps of cracks following earthquakes, they arise in surface physics, in the geo metry of rough surfaces, and in many other (sometimes unexpected) places. Mandelbrot’s idea, that Nature’s geome try is often fractal, has indeed developed into a very useful scientific discipline.

What is fractal geometry in physics?

One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. The concepts of self-similarity and scale invariance have arisen independently in several areas.

How is fractal geometry related to mathematics?

fractal, in mathematics, any of a class of complex geometric shapes that commonly have “fractional dimension,” a concept first introduced by the mathematician Felix Hausdorff in 1918. Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.

Are atoms fractal?

Atoms arrange themselves in regular patterns that do not follow fractal rules. Electrons have orbits that have a nice, regular geometry. None of this fractional dimensional stuff here, thank you very much.

Who discovered fractal geometry?

Benoit Mandelbrot
Benoit Mandelbrot was an intellectual jack-of-all-trades. While he will always be known for his discovery of fractal geometry, Mandelbrot should also be recognized for bridging the gap between art and mathematics, and showing that these two worlds are not mutually exclusive.

Are all fractals self-similar?

Simply put, a fractal is a geometric object that is similar to itself on all scales. If you zoom in on a fractal object it will look similar or exactly like the original shape. This property is called self-similarity. On all scales the Sierpenski triangle is an exactly self-similar object.

What is a fractal pattern?

Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.

What can fractal geometry accomplish beyond Euclidean geometry?

Unlike squares and circles, fractals are broken into irregular fragments. This new form of a non-Euclidean geometry enables us to measure fragmented structures.

Is universe a fractal?

The universe is definitely not a fractal, but parts of the cosmic web still have interesting fractal-like properties. For example, clumps of dark matter called “halos,” which host galaxies and their clusters, form nested structures and substructures, with halos holding sub-haloes and sub-sub-halos inside those.

What is a quantum fractal?

Now physicists at MIT and elsewhere have for the first time discovered fractal-like patterns in a quantum material — a material that exhibits strange electronic or magnetic behavior, as a result of quantum, atomic-scale effects.

Is there a relationship between quantum transport and fractality?

However, the interplay between quantum transport and fractality is still waiting for experimental exploration, despite abundant theoretical studies at non-integer dimensions 32, 33, 34, 35, 36 and pioneering experiments in integer-dimensional ordered 37, 38, 39, 40, 41, disordered 42, 43, 44, 45 and non-Hermitian lattices 46.

What is an example of a fractal pattern?

The X-ray-focusing lens used in the experiment is based on a design used in lighthouses for centuries. The repeating patterns in a snowflake are a classic example of beautiful, geometric fractals. Now MIT scientists have discovered fractal-like patterns in the magnetic configurations of a quantum material for the first time.

What can photonic lattices tell us about quantum transport dynamics?

Photonic lattices based on femtosecond-laser direct-writing techniques, on the other hand, are shown to be the ideal system to investigate quantum-transport dynamics, since they enable the precise design and fabrication of three-dimensional structures 52, 53.