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In traditional mathematics or computer science courses we learned about geometry - shapes in 1, 2 or 3 dimensions. We learned about circumferences, areas, distances between points on a line and vectors to represent lines and shapes.
However, a time in our lives arrives when we start to question how those shapes relate to the real world and could these lines and shapes indeed be used to describe the natural world?
The books in our bookshelves are cuboids, the apples in our fruit bowls are spheres, yet the trees outside our windows have branching patterns that repeat themselves at smaller scales with the new twigs and leaves they produce. If we think about our own bodies, we realize that with every breath we take our lungs have the capacity to expand and fill with oxygen as and when required. They too follow a similar pattern - the bronchi branch off into bronchioles which then branch into alveoli. On further investigation we note that our brains, our circulatory and nervous systems follow similar patterns. Don’t forget, the broccoli we ate for dinner last night or the repetition, rotation and expansion of a snail shell home, once the contents have been removed. Then there are the lightening bolts that branch off in similar ways, the way ice freezes on windscreens, tidal marks etched onto a seashore, coastal outlines and river tributaries as seen from satellite imagery.
These organic and evolving shapes cannot be described by the ideal world presented to us in traditional mathematics textbooks. We call these geometrical, branching or algebraic shapes found in nature - fractals - and they form an important aspect of computational thinking being taught in STEAM.
An observation of fractals in nature helps us to understand how the incredible complexity of natural forms all around us come about by simple repetition of objects at smaller and smaller scale. What we have learnt since the 1980s and the advent of high-powered microscopes and computer processing power is that the deeper we explore their intricacy and beauty, the more self-repeating patterns we find. Part of the mystery and intrigue is that they are infinite as far as the eye or technology allow us to see.
Observing is one thing, but creating is another. How can we use this wonder to innovate? Unlike the images in geometry that use vectors to describe a shape, fractals are described as algorithms. By using advances in data science and machine learning, we are now able to gather and analyze vast amounts of data that allow us to photograph scenarios, model new ones and make informed diagnoses and predictions.
For example, in medicine, doctors are starting to look closely at fractal patterns in blood vessels inside of cancerous tumors to learn about how the tumors grow.
They use computed tomography scans to show us the health of lungs. A healthy lung shows clean fractal pathways. An unhealthy lung shows distorted pathways.
Likewise in ophthalmology, an analysis of fractal pathways can be used in the diagnosis of retinal disease.
In bacteriology, observation of the ways in which bacteria grow can help us predict their onward growth.
Much research is currently being conducted in the fractal variance of brain waves in affective and anxiety disorders. Given that neurons are responsible for all we perceive, imagine, remember, this is hardly an insignificant area of study!
Other than nature, we too find that the systems in which we live exhibit fractal pathways.
In data compression science, images are compressed into a group of self-repeating and reducing patterns. Although finite, the fractal algorithm is drawn from nature.
In some microprocessor chips, cooling circuits use fractal branching patterns.
In compact antennas which receive radio signals across a range of frequencies, fractal designs are used.
Studying the physical structure of an ancient city can tell us something about the history of that city and the human activity contained within its 'walls'. Where fractal designs have been used e.g. a city contains towns, towns have villages and villages have neighbourhoods that are each replicas of the original but on a smaller scale, these cities have been found to be more pedestrian-friendly and human-scaled than those that have relied on other geometrical structures.
Take a walk on the wild side this holiday. Go out into nature, and look for fractals. Find, draw, photograph and share those self-repeating patterns. Be open to receiving new inspiration for your next innovative project...
ANNA SIKORA, Enseignante Informatique, EduTech & STEAM / MIT Lead