Our brains are composed of cells called neurons, and their combined activity is believed to generate consciousness. Each neuron contains microtubules, which transport substances to different parts of the cell. Microtubules are structured in a fractal pattern which would enable quantum processes to occur. Fractals are neither two-dimensional nor three-dimensional, but are instead some fractional value in between. In mathematics, fractals emerge as patterns that repeat themselves infinitely, generating what is seemingly impossible: a structure that has a finite area, but an infinite perimeter.

This might sound impossible to visualise, but fractals actually occur frequently in nature . The florets of a cauliflower or the branches of a fern , are both made up of the same basic shape repeating itself over and over again, but at smaller and smaller scales. Fractals also feature in the enchanting repeating artworks of MC Escher and Jackson Pollock , and they’ve been used for decades in technology, such as in the design of antennas . These are all examples of classical fractals – fractals that abide by the laws of classical physics rather than quantum physics.

It’s easy to see why fractals have been used to explain the complexity of human consciousness. Because they’re infinitely intricate, allowing complexity to emerge from simple repeated patterns, they could be the structures that support the mysterious depths of our minds.

But if this is the case, it could only be happening on the quantum level, with tiny particles moving in fractal patterns within the brain’s neurons. That’s why Penrose and Hameroff’s proposal is called a theory of “quantum consciousness”.

Advanced technology means we can now measure quantum fractals in the lab. In recent research involving a scanning tunneling microscope, electrons are carefully arranged in a fractal pattern, creating a quantum fractal.

Then the wave function of the electrons were measured, which describes their quantum state, they too lived at the fractal dimension dictated by the physical pattern they’d made. In this case, the pattern used on the quantum scale was the Sierpiński triangle , which is a shape that’s somewhere between one-dimensional and two-dimensional.

Using state-of-the-art photonics experiments, they were able to reveal the quantum motion that takes place within fractals in unprecedented detail. They achieved this by injecting photons (particles of light) into an artificial chip that was painstakingly engineered into a tiny Sierpiński triangle. Injected photons at the tip of the triangle spread throughout its fractal structure in a process called quantum transport. They repeated this on two different fractal structures, both shaped as squares rather than triangles.

Our observations from these experiments reveal that quantum fractals actually behave in a different way to classical ones. Specifically, we found that the spread of light across a fractal is governed by different laws in the quantum case compared to the classical case. This knowledge of quantum fractals could provide the foundations for scientists to experimentally test the theory of quantum consciousness. If quantum measurements are one day taken from the human brain, they could be compared against our results to definitely decide whether consciousness is a classical or a quantum phenomenon.

This work could also have profound implications across scientific fields. By investigating quantum transport in our artificially designed fractal structures, we may have taken the first tiny steps towards the unification of physics, mathematics and biology, which could greatly enrich our understanding of the world around us as well as the world that exists in our heads.