A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal.
A famous example is the boundary of the Mandelbrot set.
Fractal curves in nature
Fractal curves and fractal patterns are widespread, in
nature, found in such places as
broccoli,
snowflakes, feet of
geckos,
frost crystals, and
Lightning strike.
See also Romanesco broccoli, dendrite crystal, trees, fractals, Hofstadter's butterfly, Lichtenberg figure, and self-organized criticality.
Dimensions of a fractal curve
Most of us are used to mathematical curves having dimension one, but as a general rule, fractal curves have different dimensions,
also see fractal dimension and list of fractals by Hausdorff dimension.
Relationships of fractal curves to other fields
Starting in the 1950s Benoit Mandelbrot and others have studied
self-similarity of fractal curves, and have applied theory of fractals to modelling natural phenomena. Self-similarity occurs, and analysis of these patterns has found fractal curves in such diverse fields as
economics,
fluid mechanics,
geomorphology,
human physiology and
linguistics.
As examples, "landscapes" revealed by of in connection with Brownian motion, , and shapes of all relate to fractal curves.
Examples
See also
External links
