http://mathworld.wolfram.com/images/eps-gif/Fractal1_1000.gif

Definitions of fractals

Fractals are a visual metaphor for emergent processes. They demonstrate how the iterations of a pattern / the pattern of iterations can give rise to new patterns. These new patterns emerge at a greater scale but only exist as a function of the original pattern at a lesser scale.


Fractals | Eric Weisstein

http://mathworld.wolfram.com/images/eps-gif/Fractal1_1000.gif

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same “type” of structures must appear on all scales.

REFERENCE
Fractals | Eric Weisstein


Fractal | Wikipedia

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern…Fractals can also be nearly the same at different levels…Fractal also includes the idea of a detailed pattern that repeats itself.

REFERENCE
Fractal | Wikipedia


What are fractals? | Fractal Foundation

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals…can be generated by a computer calculating a simple equation over and over.

REFERENCE
What are fractals? | Fractal Foundation

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