Fractal patterns spotted in the quantum realm

From thunderous mountain landscapes viewed from above to the erratic trajectories of Brownian motion, fractal patterns exist at many scales in nature. Physicists believe that fractals also exist in the quantum world, and now a group of researchers in the US has shown that this is indeed the case.

Scientists from Princeton University in the US have revealed that fractal patterns also exist at the scale of individual atoms in a solid. And the key to this effect is a sudden transition where a material changes from a metal to an insulator. At this transition, the waves associated with individual electrons go from being extended across the whole system to being localized at lattice sites.

At this metal–insulator transition the electron waves become squashed together. They begin to affect each other in a complicated network of constructive and destructive interference, which results in a fractal pattern. The researchers were able to observe this effect using a scanning tunnelling microscope (STM), which provided the atomic scale resolution.

The material used was the ferromagnetic semiconductor gallium arsenide doped with up to 5% manganese, chosen because the researchers are interested in efficient ways of turning a semiconductor into a magnet. Indeed, doping gallium arsenide in this way has become a popular approach in the burgeoning field of spintronics – electronics that exploits the spin of particles as well as their charge. Spintronics has the potential to boost the speed of computing and electronics.

Talking about his research, scientists admit that observing these fractals was not the primary aim of their research. The team intend to develop their research by comparing the collective versus individual behaviour of electrons in their system and how this influences the spatial patterns. The bigger picture of this research is to connect these patterns with theories of magnetism to advance both fundamental research and the development of spintronics applications.

Fractals in the biological sciences

Biologists have traditionally modeled nature using Euclidean representations of natural objects or series. They represented heartbeats as sine waves, conifer trees as cones, animal habitats as simple areas, and cell membranes as curves or simple surfaces. However, scientists have come to recognize that many natural constructs are better characterized using fractal geometry. Biological systems and processes are typically characterized by many levels of substructure, with the same general pattern repeated in an ever-decreasing cascade. For instance, the bronchi of the human lung are self similar over 15 successive bifurcations

At each level in the human body we can see how fractals are involved with the communication, transportation or transformation of energy, matter and information in and out of the mind/body or between its various subsystems. This is the hallmark of open, complex, self-organizing systems existing in far-from-equilibrium conditions.

At the biological level, our skin is pocked with fractal pores that negotiate the transportation of oxygen inside and of water and toxins outside. Wrinkles, physical evidence of our unique histories becoming etched into our faces, are fractal as well. So too are the pattern of animal markings, such as spots and stripes on leopards and zebras, lending each animal a unique fractal signature.

Many of our internal organs display fractal structure. These include the lungs, which bring air into the body; branching patterns of our arteries and veins, which circulate blood and nutrients throughout the body; the intestines, which transport waste outside; and the brain, our executive center for communication, transportation, navigation and broadly modulating relations between internal and external worlds. For instance, the bronchi of the human lung are self similar over 15 successive bifurcations.

Scientists discovered that the basic architecture of a chromosome is tree-like; every chromosome consists of many 'mini-chromosomes', and therefore can be treated as fractal. For a human chromosome, for example, a fractal dimension D equals 2,34. Self-similarity has also been found in DNA sequences. In the opinion of some biologists, fractal properties of DNA can be used to resolve evolutionary relationships in animals.

Mini-dictionary

UNIT 1. Fractals

a fractal	фрактал
a miniature replica	мініатюрна копія
to coin the term	вигадати термін
to undergo iteration	зазнавати ітерації
a feedback	зворотний зв'язок
recursion / recursive	рекурсія /рекурентний, рекурсивний
self-similarity	самоподібність
non-integer dimension	дробова розмірність
statistical quantity	статистична величина
magnification	збільшення
soil	ґрунт
to classify	класифікувати
to fill space	заповнювати простір
at different scales	в різних масштабах
deterministic	детермінований
stochastic	стохастичний
iterated function system	система ітерованихфункцій
distorted	викривлений, деформований
recurrence relations	рекурентні відношення
to preserve	зберігати
complex number	комплексне число
to approximate to a degree	значно наближатися
a list	список, перелік
craft	ремесло
to appear identical	виявитися ідентичними
lightning bolt	спалах блискавки
the respiratory system	дихальна система
the circulatory system	кровоносна система

Mini grammar