Self-Similarity

Fractal theory is grounded in geometry and dimension theory. Geometrically, fractals are independent of scale and appear equally detailed at any level of magnification. This property, called self-similarity, means that any portion of a self-similar fractal curve, if blown up in scale, would appear identical to the whole curve. In other words, if we shrink or enlarge a fractal pattern, its appearence remains unchanged. This repetition of a pattern at all scales, no matter how small, is exhibited by many natural objects. For example, imagine that you are in space looking at the coastline of Britain. As you approach the Earth, the coastline still looks like a coastline. No matter how close you get to Britain's shore, the coastline appears equally complex. Even after you land your spacecraft and get down on your hands and knees with a microscope at the water's edge, the coastline still looks jagged and irregular.