Why should fractal geometry matter to those of us who are not mathematicians? First of all, fractals give human beings a new way to look at the universe. When we can describe something, we can see it better than if we cannot describe it. Because we are better able to see the natural world, fractals enable us to have a deeper relationship to the natural world.
It reminds me of learning to read a book. In order to read, we need to understand the patterns of squiggly lines that form the letters of the alphabet. And then we need to understand how those squiggly lines are combined in multiple ways to form words, and then sentences, and so on. A person who cannot read may look at a book, and it might seem beautiful, or there might be pictures in it to be curious about, but that person cannot understand what it means. When we learn to read the patterns of squiggly lines, the book becomes a doorway into a whole story, and suddenly we have access to a wealth of ideas and thoughts and understandings.
The natural world is like a sacred book; it is the place where we search for truth and beauty and goodness. We might say that the universe itself is our bible. We don’t have to understand the world to appreciate its beauty. Even a baby can laugh with delight at the bright colors of flowers, or try to catch a butterfly. But the more we understand the natural world, the deeper can be our appreciation, and the more its mystery opens up to us. Fractals help us to read the book of the universe.
Fractals give us a way to measure and describe the complex patterns in the natural world. Fractal geometry, in fact, reveals to us the inherent patterning that permeates the universe. A fractal is a pattern that repeats itself, from an infinitely small scale to an infinitely large scale. Complex entities are created from simple designs extended out to many dimensions. We see in the patterns and shapes of nature that there is self-similarity at all levels.