Fractal Lightning Another naturally occurring fractal pattern is a lightning bolt. As Benoit Mandelbrot noted in the opening quotation, lightning does not travel in straight lines. Rather, it follows a chaotic, jagged path, formed as the huge charge separation built up in the sky suddenly breaks down. The majority of a lightning bolt is generally hidden in a cloud, much as an iceberg hides beneath the ocean. Lightning can be very large, spanning several kilometers, but it is formed in microseconds.
Just as we could say that the fractal dimension of a broccoli is 2. This number is greater than 1, which indicates that a lightning bolt trajectory fills more space than an ordinary curve. Eduardo Ros. Climate change conferences. Why do we age? If you look at a small section of a mathematical fractal, the section will be identical to the whole object. And if you were to select an even smaller piece from the first section and magnify it, this piece would also duplicate the whole.
The image below shows a classic mathematical fractal, the Sierpinski Triangle, or Sierpinski Gasket. Make a fractal pattern on clear tape see Alternative Construction above. Stick the resulting two pieces of tape to a piece of paper, and create art or poetry inspired by the fractal images. The Sierpinski Triangle and the Cantor Set, or Cantor Dust, are two classic fractals whose algorithms set of instructions for their construction can be easily understood.
Look these up to get a nice idea of how a mathematical fractal is generated. The word fractal was first used in by the Polish-born mathematician Benoit Mandelbrot — The word derives from the Latin frangere to break and fractus broken, uneven. Mandelbrot spent much of his working life in both France and the United States and is credited with the development of fractal geometry. His various studies included stock-market fluctuations, the turbulent motion of fluids, and the distribution of galaxies.
Fractals helps us to understand many different areas of science, including crystal growth, earthquake processes, meteorology, and polymer structure, to name just a few. Fractals are particularly significant in the field of chaos theory , which seeks to explain apparently random behavior that occurs within a system. San Francisco: W. Freeman, Berlin: Springer-Verlag, Air trapped between two pieces of clear plastic produces rainbow-colored interference patterns.
Attribution: Exploratorium Teacher Institute. Connect with us! Get at-home activities and learning tools delivered straight to your inbox. The Exploratorium is a c 3 nonprofit organization. Fractal Patterns Make dendritic diversions and bodacious branches. Grade Bands:. Scale, Proportion, and Quantity. Systems and System Models.
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