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Even 2000 times magnification of the Mandelbrot set uncovers fine detail resembling the full set. 
A fractal that models the surface of a mountain (animation)

Barnsley's fern computed using an Iterated function system

Photograph of a romanesco broccoli, showing a naturally occurring fractal

.A fractal is formed when pulling apart two gluecovered acrylic sheets.^
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.High voltage breakdown within a 4″ block of acrylic creates a fractal Lichtenberg figure.^

.Fractal branching occurs in a fractured surface such as a microwaveirradiated DVD.^
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A "woodburn" fractal

A magnification of the phoenix set

A fractal flame created with the program Apophysis

Fractal made by the program Sterling

[[File:thumbright200pxA Sierpinski triangle, after 7 iterations.]]
A fractal is any equation or pattern, that when seen as an image, produces a picture, which can be zoomed into infinity and will still produce the same picture. The word fractal was made by Benoît Mandelbrot in 1975 from the Latin word fractus, which means "broken" or "fractured". A simple example is a tree that branches infinitely into smaller branches, and those branches into smaller branches and so on. Fractals are not only beautiful, but also have many practical applications.
There are many types of fractals, made in a large variety of ways. One example is the Sierpinski triangle, where there are an infinite number of small triangles inside the large one. Another example is the Mandelbrot set, named for Benoît Mandelbrot. The Sierpinksi triangle is constructed using patterns, but the Mandelbrot set is based on an equation.
There are also many natural examples of fractals in nature including trees, snowflakes, some vegetables and coastlines.
Some fractals exist only for artistic reasons, but others are very useful. Fractals are very efficient shapes for radio antennas and are used in computer chips to efficiently connect all the components.
Here are sentences from other pages on Fractal, which are similar to those in the above article.
