Fractals

Fractals are infinitely complex and beautiful patterns produced through the repetition of a simple formula or shape, patterns which often appear rough or chaotic and which can be found everywhere in nature (the surface of the sea, the edge of a cloud, the dancing flames in a wood fire). I have written about them briefly before.

What appeals to us in such patterns, perhaps, is the combination of simplicity and complexity. They allow our minds scope to expand, and our imaginations to take off in the direction of the infinite, but at the same time to rest in a unity. It is similar to the reason we love science. Scientists are seeking the simple secret at the heart of the complex - the formula or combination of universal laws that governs all of reality and explains why it works or appears the way it does.

Something similar is happening in art, when the artist seeks unity of concept or meaning or mood in a complex scene or sight or landscape.

Not all beauty is produced by these "recursive algorithms" or the repetition of self-similarity at different scales of magnitude. Sometimes a pattern is just there in the thing and does not repeat itself. But beauty always has something to do with order, which means the finding of a unity of form in something complex - a balance between the Many and the One. The finding of unity gives us joy (which is why we call it beautiful) because it enables us to recognise the Self in the Other, outside ourselves. It causes us to expand our boundaries to include the other thing as grasped and understood, or at least as situated in a relationship to us. Fractal patterns are a version of that experience. We sense the unity, but because it is expressing itself as never-ending complexity, it never gets boring.

Therefore all beauty, including fractal beauty, reminds us of God, who is both infinitely simple (in himself, as pure love) and yet infinitely complex (in what he contains and creates).

Simplexity

The world as a whole is complex, but it is also a unity. It is “simplex”, founded on simple principles. Poets, painters, scientists and mathematicians are all searching for simplexity in their own way. Aesthetic pleasure is very largely the delight we feel in seeing order, meaning and relationship – the beauty that Coleridge called unity in variety. But it has to be an order unforced, seemingly spontaneous, rather than brutally imposed upon the material. The world as a whole is beautiful in just this sense.

Modern science describes the world as to a large extent “self-organizing”, because sophisticated and unpredictable patterns are now thought to emerge spontaneously from the indefinite repetition of simple algorithms. Furthermore they do so without violating the law of entropy. Evolution is then held to account for the refinement of those patterns through the process of selection. None of this - if true - is incompatible with theism (although it makes Intelligent Design look a bit foolish). The Christian God is the principle of existence itself, the creator without whom there would be nothing either simple or complex to admire. (For the compatibility of theistic faith with an up-to-date cosmology see Stephen Barr’s Modern Physics and Ancient Faith, reviewed here.)  If with complexity emerges unpredictability, this merely highlights the possibility of a higher-level order we call providence, governing coincidence and chance. God is the principle of order, and thus the ever-present source of unity as well as diversity.

If science interests you, take this awesome trip through the known universe. (The image above, by the way, is a fractal from Wikimedia Commons. For more on fractals see this clip on fractals in Africa.)