Fractals – a glimpse into divine relationships

‘God is love’(1 John 4:16) in which case the place to find God is in relationships – within the Trinity, between God and all living things and within us - or asDavid Cunnigham puts itin These Three are One (Wiley-Blackwell, 1998),‘God is relation … without remainder’. It really is pointless trying to see God as some entitybeyond Jesus, a bearded pensioner, a holy icon, a Bruce Almighty. No picture is adequate, no geographic location, no time, no texture or material is God – just relationships. God is relationship.

So are fractals. Theyarean infinity of multi-dimensional beautyeach created by the simplest of mathematical functions, or relationships. But ignore the long words and the maths, fractals are built from simple relationships between shapes – in the example below - betweentwo rectangles and a sheet of A4. And, because of that, theyprovide a remarkable parallel insight intoGod’s love. In both fractals and love, incredible beauty stems from the activity in simple relationships – ‘the clouds disperse, the shadows fly, the invisible appears in sight and God is seen by mortal eye’ (Charles Wesley).

So – have a go - build your own fractal …. it’s called the Chaos Game.

Take a blank sheet of paper and, very lightly, draw two large rectangles on it, any angle, anywhere you like, overlapping or not. Each rectangle should be smaller than the sheet itself though their corners can disappear off the edge of the sheet. For each rectangle, label one of the sides as the top. Then, with a pen, put a first small dot anywhere on the sheet.

Randomly choose either one of your drawn rectangles. Now the difficult bit: note where that dot is with respect to the whole sheet of paper, and put another dot inside your chosen rectangle, positioning it as if your chosen rectangle were the whole sheet. So, for example, if your dot was near the top-right corner of the whole sheet, your next dot is near the top-right corner of the chosen rectangle.

Do that last paragraph 100+ times, each time randomly choosing one of the two rectangles and using the latest dot. If you persist, your dots will be attractedinto some clusters on the sheet that will slowly form a fractal dot-picture –often something beautiful, entirely determined by the relationships between the rectangles and the sheet of paper.

Beauty comes more spectacularly when a computer is used to render them with millions of dots, using some convention to colour each pixel on the screen. Each new dotadds more to the beauty. Each activity, rooted in our loving relationships, builds something more beautiful.

Fractals are only 2D on paper, but their simplicity can provide computer game writers with a tool to create complex 3D landscapesevolving over time. Depending on the relative position, number and sizes of the rectangles, the dot-pictures can look like leaves, trees, flowers, corals, ferns, mountains, coastlines, honeycombs, dragons, lichen, flames, clouds and hundreds more images of nature. The two rectangles above generate something like a feather:

Zoom in on a fractal and you discover its complexity isinfinite – so with small enough dots on a large enough piece of paper you can go on adding dots forever, colouring and re-colouring. It would take an eternity to explore fully any fractal, we don’t have enough light-sensitive cells in our eyes, nor enough neurons in our brains to hold the detail. Instead we look at the beautiful pictures - limited to both the resolution of a computer screen and to what we can understand – it’s like seeing the infinite through a glass, darkly(1 Cor 13:12). Yet, what we see, we recognise as having some meaning, some pattern. The glorious picture is a human-comprehensible incarnation of the vast and inconceivable. Literally the logic takes on a shape - becomes flesh- and we behold its glory(John 1:14)- all fromthe relationships between the two rectangles and a sheet of A4 – their position and size showing where to put the next dot, where the next crumb of activity adds to the beauty of the picture.

Beauty comes from each activity in loving relationships with God and with others. Do nothing and you see nothing. Only by engaging with love/doing-the-dots can you really begin to hold the breadth, depth, and height of the infinite.

Also fractals are beautiful because they are made from ever smaller and similar versions of themselves. The pictures (and web site)illustrate this feature –called self-similarity. Nature often works like that. A fern leaf seems to contain small versions of itself, fragments of coastline look like a whole coastline, a cauliflower is a bunch of cauliflowers! The smaller versions are contained in the larger, yet, because a fractal is infinite, each of the parts is just as wonderful and complex as the whole.

Such self-similarity is alsofeature of God and the kingdom. I am in the Father, and the Father is in me (John14:11), Live in me and I’ll live in you (John 15:4), This is my body (Luke 22:19), You are the body of Christ(1 Cor 12:27) and God in Christ (Rom 6:11) all resonate the self-similarity of the persons of God and of us in Christ. And Jesus’ wordsI am the vine and you are the branches (John 15:5),speak of us becoming similar to him, contained in him, structurally part of him, being him in the world, just asa branch of a vine looks like a whole vine. Self-similarity is key, just as relationships are key. A fractal is self-similar, defined by its relationships.

Freewill is also important. The chaos game above, needsyou, each time you place a dot to make a random choice about which of the two rectangles you are going to use. Wherever you start from (your first dot), eventually your dots will become part of the shape – the mathematicians use the word attractor because the journey of the dots always finds its way there. Doing love, being active in Godly relationships, brings you into the kingdom. Anyone who loves is a child of God (1 John 4:7).

The whole thing does not work if you keep choosing the same rectangle. Then there is no beauty and the picture fails. It is the chaotic activity we have in love with relations, with neighbours, with ourselves and with God – the whole community around us - that creates the beauty. Life needs some chaos, we need to keep all the balls in the air!

Experiencing the infinite, overwhelms us – but we definitely need that overwhelming from time to time. Fractals do that. It is as if I am somewhere holy when I zoom into a new fractal: where simple relationships underpin the glorious. Grasp active relationships of love and suddenly you have in your heart the immensity of God. Try a journey into the infinite for yourselfon my ecclesiastical (!) fractal website:splat.co.nr/chaos

Adrian Low

Revd. Adrian Low is emeritus professor of computer education at Staffordshire University and Assistant Curate of Abbots Bromley, Blithfield, Colton, Colwich and Great Haywood.

Currently about 1000 words.