Fractals

In mathematics a fractal is an abstract object used to describe and simulate naturally occurring objects. Artificially created fractals commonly exhibit similar patterns at increasingly small scales. It is also known as expanding symmetry or evolving symmetry. If the replication is exactly the same at every scale, it is called a self-similar pattern.

An example of this is the Menger Sponge. Fractals can also be nearly the same at different levels. This latter pattern is illustrated in small magnifications of the Mandelbrot set. Fractals also include the idea of a detailed pattern that repeats itself.

Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees.[48] Phenomena known to have fractal features include:

River networks
Fault lines
Mountain ranges
Craters
Lightning bolts
Coastlines
Mountain goat horns
Trees
Algae
Geometrical optics
Animal coloration patterns
Romanesco broccoli
Pineapple
Heart rates
Heart sounds
Earthquakes
Snowflakes
Psychological subjective perception
Crystals
Blood vessels and pulmonary vessels
Ocean waves
DNA
Soil pores
Rings of Saturn
Proteins
Surfaces in turbulent flows