Mandelbrot later also investigated shapes distorted in some way from one length to another. These fractals are now called nonlinear, since the relationship between their parts is subject to change. The most intriguing of the nonlinear fractals thus far has been the Mandelbrot set. Not all fractals are self-similar or at least not exactly so, but most exhibit this property. This reiteration of irregular details or patterns occurs at progressively smaller scales and can, in the case of abstract mathematical entities, continue indefinitely, so that each part of each part, when magnified, bears an exact resemblance to the whole, the likeness continuing with the parts of the parts and so on ad infinitum .
Fractal geometry describes objects that are self-similar, or scale symmetric.
Instead a rough, jagged quality is maintained at every scale at which an object can be examined. This fractal character can be seen in such objects as snowflakes and trees. The rough shape revealed at one length scale bears only an approximate resemblance to that at another, but the length scale being used is not apparent just by looking at the shape. Fractint is a classic fractal generator. Fractal Music Composition Software .