D Is Not A Unique Descriptor
As is the case with dimensions determined for lines, squares, and cubes, fractal dimensions are general descriptors that do not uniquely define patterns. The value of D for the Koch fractal discussed above, for instance, quantifies the pattern's inherent scaling, but does not uniquely describe nor provide enough information to reconstruct it. Many fractal structures or patterns could be constructed that have the same scaling relationship but are dramatically different from the Koch curve, as is illustrated in Figure 6.
For examples of how fractal patterns can be constructed, see Fractal, Sierpinski triangle, Mandelbrot set, Diffusion limited aggregation.
Read more about this topic: Fractal Dimension
Famous quotes containing the word unique:
“The unique eludes us; yet we remain faithful to the ideal of it; and in spite of sense and of our merely abstract thinking, it becomes for us the most real thing in the actual world, although for us it is the elusive goal of an infinite quest.”
—Josiah Royce (1855–1916)