Harmonic Fractals

Exploring the mathematics built into nature.

Welcome to the world of fractals.

Fractals appear everywhere in nature.

Some common characteristics are shared between many objects in nature. We often find that these characteristics can be mathematically defined. Isaac Newton, Albert Einstein, and many others have shown us how the laws of physics are mathematically defined, but there are many other rules that God has also made nature to follow.

One rule common to many objects is that of repetition. For instance, one cloud looks fairly similar to another; one island resembles many other islands in it's outline; one tree looks fairly similar to other trees, especially trees of the same variety.

Another rule of nature is that of self similarity. Not only are things similar to each other they also tend to be similar to themselves at other scales. A tree may look similar to one of it's branches stuck into the ground. A large cloud may have a similar outline to a smaller cloud or to a piece of the large cloud.

Finally we have the rule of Chaos. Within many systems there comes a point where the rules seem to break down. Something that seems to have been working together with a nice orderly repetitions and subdivisions suddenly seems to become chaotic and disordered. Under closer investigation, though, we often find that order still applies, it is just a little more subtle.

Wherever we look from the smallest molecules to the arrangement of galaxies reflects the order, harmony, and beauty that God has placed within mathematics, physics, and nature.