Publication: Fractals on a benchtop: observing fractal dimension in a resistor network
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2022-09
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American Association of Physics Teachers
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Abstract
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two dimensional, and a volume is three dimensional. However, following the work of Mandelbrot, systems with a fractional dimension, "fractals," now play an important role in science. The novelty of encountering fractional dimension, and the intrinsic beauty of many fractals, has a strong appeal to students and provides a powerful teaching tool. I describe here a low-cost and convenient experimental method for observing fractal dimension, by measuring the power-law scaling of the resistance of a fractal network of resistors. The experiments are quick to perform, and the students enjoy both the construction of the network and the collaboration required to create the largest networks. Learning outcomes include analysis of resistor networks beyond the elementary series and parallel combinations, scaling laws, and an introduction to fractional dimension.
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© 2022 American Association of Physics Teachers
I would like to thank Alan L. Smith for inspiring this investigation. This work was supported by Spain's
MINECO through grant FIS2017-84368-P.