If the replication is exactly the same at every scale, it is called a self-similar pattern.
Fractals are different from other geometric figures because of the way in which they scale. Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in).
Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). But if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer.
This power is called the fractal dimension of the fractal, and it usually exceeds the fractal's topological dimension.
With this app, you can create and share your own fractals. Just change the values in the configuration screen
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