For decades, fractals have aided scientists in understanding the natural and mathematical world. Now, researchers just created a fractal shape on a quantum scale.

*Scientists just built an electron-based fractal system, giving new insights about these intriguing geometric shapes at the quantum scale.*

**Fractals **are complex geometric structures, sometimes hypnotizing, with patterns repeating ad infinitum.

In the 1970s, mathematician **Benoît Mandelbrot** coined the term “fractals” and gave his name to one of the most famous abstract fractals: the **Mandelbrot set**.

In nature, we find fractals everywhere.

Fractal geometry lets the vessels of the cardiovascular system branch out efficiently into your body to deliver blood.

Plants are masters of fractal geometry to help expose their leaves and absorb as much sunlight as possible.

Trees, ferns, snowflakes, rivers, coastlines, lightning, clouds, lungs, and blood vessels are just a few examples of natural fractals.

Understanding fractals help us create complex computer models, for example. These models help us to study the evolution of clouds and predict weather patterns more accurately.

Now, researchers have taken fractals to an unprecedented scale and demonstrated that their geometric “**self-similarity**” could go deeper, down to to the **quantum level**.

#### Read More: **New Qubit System Brings Us Closer to Quantum Supremacy**

## Quantum Fractals: Electrons in 1.58 dimensions

Physicists from the **Faculty of Science** at the **University of Utrecht** (**UU**) in the Netherlands managed to scale fractal structures down to the microscopic level.

**Electrons **can align in **one dimension** as a line, or in **two dimensions** to form a sheet. They can also form into **three dimensions** and take the shape of a cube.

At each of the three states, electrons exhibit different **quantum behaviors** that serve different applications in electronics.

We know of one dimension, 2D, and 3D, and we can imagine higher dimensions, but what would a **1.58 dimension **structure even mean?

Electrons can exist in 1.58 dimensions, which is difficult to fathom from our macroscopic standpoint. The Utrecht researchers explained that:

*“Non-integer dimensions, such as 1.58, can be found in fractal structures, such as your lungs. A fractal is a self-similar structure that scales in a different way than normal objects: if you zoom in, you will see the same structure again. For example, a small piece of Romanesco broccoli typically looks similar to the whole head of broccoli. In electronics, fractals are used a lot in antennas for their properties of receiving and transmitting signals in a large frequency range.”*

## Creating New Quantum Dimensions

To investigate the quantum fractals, the Utrecht team built **nanoscale fractals **out of electrons.

Using a scanning tunneling microscope, they placed carbon monoxide molecules on a copper background. This created a ‘muffin tin’ for electrons to gather and form a fractal shape.

Electrons then took a triangular fractal shape known as a **Sierpiński triangle**, *“which has a fractal dimension of 1.58″. *The researchers observed that the electrons in the triangle actually behave as if they live in 1.58 dimensions.

*Theoretical physicist Cristiane de Morais Smith, one of the study’s supervisors, explains its significance:*

*“From a theoretical point of view, this is a very interesting and groundbreaking result,” “It opens a whole new line of research, raising questions such as: what does it actually mean for electrons to be confined in non-integer dimensions? Do they behave more like in one dimension or in two dimensions? And what happens if a magnetic field is turned on perpendicularly to the sample? Fractals already have a very large number of applications, so these results may have a big impact on research at the quantum scale. One thing is for sure: the future of electronics looks **fractastic**!”*

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