Coastline Paradox

Determining the length of a country's coastline is not as simple as it first appears, as first considered byL. F. Richardson (1881-1953). In fact, the answer depends on the length of the Ruler you use for the measurements.A shorter Ruler measures more of the sinuosity of bays and inlets than a larger one, so the estimated lengthcontinues to increase as the Ruler length decreases.

In fact, a coastline is an example of a Fractal, and plotting the length of the Ruler versus the measuredlength of the coastline on a log-log plot gives a straight line, the slope of which is the Fractal Dimension of thecoastline (and will be a number between 1 and 2).

References

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 29-31, 1991.

• Maltese Cross Curve
• Malthusian Parameter
• Mandelbar Set
• Mandelbrot Set
• Mandelbrot Tree
• Mangoldt Function
• Manifold
• Mantissa
• Map
• Map Coloring
• Mapes' Method
• Map Folding
• Mapping (Function)
• Mapping Space
• Map Projection
• Marginal Analysis
• Marginal Probability
• Markoff Number
• Markoff's Formulas
• Markov Algorithm
• Markov Chain
• Markov Matrix
• Markov Moves
• Markov Number
• Markov Process