Fractal

1. （Noun）
   
   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 – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.
   
2. （Noun）
   
   An object whose parts, at infinitely many levels of magnification, appear geometrically similar to the whole.
   
   Fractals are used in the design of compact antennas and for computer modeling of natural-looking structures like clouds and trees.
   
3. （Wikipedia）
   
   The word "fractal" often has different connotations for the lay public as opposed to mathematicians, where the public is more likely to be familiar with fractal art than the mathematical concept.
   
   The mathematical concept is difficult to define formally, even for mathematicians, but key features can be understood with a little mathematical background.
   
   The feature of "self-similarity", for instance, is easily understood by analogy to zooming in with a lens or other device that zooms in on digital images to uncover finer, previously invisible, new structure.
   
   If this is done on fractals, however, no new detail appears; nothing changes and the same pattern repeats over and over, or for some fractals, nearly the same pattern reappears over and over.
   
   Self-similarity itself is not necessarily counter-intuitive (e.g., people have pondered self-similarity informally such as in the infinite regress in parallel mirrors or the homunculus, the little man inside the head of the little man inside the head ...).
   
   The difference for fractals is that the pattern reproduced must be detailed.