Manifestation of fractals in nature: Snail shell, milky way, leaf veins and motor neuron
"All the branches of a watercourse at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream." - Leonardo da Vinci
The planet Earth has fractal river networks that transport rainfall from the land to the oceans. Like all fractals, these complex, self–similar patterns are formed by the repetition of a simple process of channel formation due to erosion. River network collects a huge amount of rainfall from a very large land area and condenses it into a small area.
Lightning does not travel in straight lines but follows a chaotic and jagged path. Lightning can be very large, spanning several miles, but it is formed in microseconds. Thunder is a fractal sound. It is caused by the superheating of air. Because the pathway of the lightning bolt is a jagged fractal in 3D space, the time it takes to reach our ears varies and hence the sound we hear is a fractal pattern.
Galaxies are the largest examples of spiral fractals known. A single spiral galaxy may contain a trillion stars. The spiral arms do not contain a greater number of stars but still the spiral arms are brighter because they contain many short-lived extremely bright stars, formed by a rotating spiral wave of star formation. The waves of star formation are made visible because they contain many young and very bright stars that only live a short time, perhaps 10 million years, as compared to the more common stars, such as our sun which live for several billion years. Hurricanes or cyclones are the largest spirals here on Earth. The plant kingdom is also full of spirals, as evidenced in many cacti, flowers, fruit, pinecones, etc. A nautilus shell is another example and in this, a simple combination of rotation and expansion creates the spiral. (The figures in this page depicts the patterns in nature. In the regularity of eclipses, the arrangement of seeds in the head of a sunflower, or the spiral of a Nautilus shell, nature exhibits periodic patterns. This principle exactly matches with the arrangement of electrons in atoms which recurs periodically, which causes many properties of the elements to recur periodically and, thus, allows us to predict physical and chemical behavior.)