Fractals are special mathematical structures that are present in many areas of life. These ubiquitous patterns can have profound psychological effects on people's perception and mood. In this blog post we will examine what exactly a fractal is, how it psychologically influences the observer, and provide some examples of where we can encounter these forms in everyday life.
What is a Fractal? A fractal is a geometric shape that repeats itself. The name "fractal" comes from the Latin word "fractus" which means a broken or irregular shape. Fractals are known for being detailed and complex, even under strong magnification. Fractals are not only interesting in mathematics but also appear in nature, such as the branches of trees, the delta systems of rivers, or the microscopic structure of snowflakes.
Mathematically, fractals are shapes whose Hausdorff dimension* (also known as fractal dimension), is not an integer. This means that these shapes are more complex than traditional geometric shapes (e.g., squares, circles, or triangles). These structures are created in mathematics using repetitive algorithms, allowing their complexity to increase infinitely.
Fractals can influence human emotions and mood. Psychological research suggests that viewing fractal patterns can reduce stress and increases relaxation. This phenomenon can be explained by the fact that fractals are often encountered in nature. The complexity and repetition of fractal patterns have a calming effect on the human psyche, which can help alleviate everyday stress.
Since fractals can stimulate the parts of the brain responsible for aesthetic perception and pattern recognition, observing fractals has a soothing effect on the observer. The use of fractal art makes the environment in which we spend our days more friendly. This type of visual stimulation can help improve concentration and increase mental clarity. Some studies suggest that immersing oneself in fractal patterns can enhance creative thinking and facilitate the emergence of new ideas.
Since nature is structured fractally, we can easily notice fractals in our surroundings. Clouds often exhibit fractal-like behavior, where the complexity and arrangement of smaller cloud formations reflect larger patterns. Fractal-like patterns also can be found in beach sand and waves, which are formed due to the natural movement of tides and water. And who isn't mesmerized by the sight of the starry sky? The repetitive patterns of galaxies and nebulae exhibit fractal characteristics.
These natural examples not only provide aesthetic pleasure but also serve as a reminder of the wonders of nature. In today's busy world, it's difficult to spend more time in nature, but we can always hang a fractal print on the wall, such as those created by fractal artist Bora Zrinyi, and it will have almost the same positive effect on our mental health.
Fractals are an integral part of nature and, through their psychological effects, can directly connect us with the marvels of the natural world.
* What is an example of a Hausdorff dimension? - Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension. For example, the Cantor set, a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3) ≈ 0.63. Wikipedia
