IF "GOD is love" (1 John 4.16), then the place to find God is in
relationships - within the Trinity, between God and all living
things, and within us - or, as David Cunnigham puts it in These
Three are One (Wiley-Blackwell, 1998), "God is relation . . .
It really is pointless trying to see God as some entity beyond
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. They are an infinity of multi-dimensional
beauty each 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, between two rectangles and a sheet of A4. And, because of
that, they provide a remarkable parallel insight into God'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 you can have a go, and build your own fractal: it is 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,
although 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-hand corner of
the whole sheet, your next dot is near the top right-hand corner of
the chosen rectangle.
Repeat that last paragraph 100plus times, each time randomly
choosing one of the two rectangles and using the latest dot. If you
persist, your dots will be attracted into some clusters on the
sheet which will slowly form a fractal dotpicture - 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 the images with millions of dots, using some convention to
colour each pixel on the screen. Each new dot adds 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
writers of computer game with a tool to create complex 3D
landscapes evolving 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 birds flying in formation.
ZOOM in on a fractal, and you discover its complexity is
infinite. So, with small enough dots on a large enough piece of
paper, you can go on adding dots for ever, 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 by both the resolution of
a computer screen and to our own understanding, it's like seeing
the infinite through a glass, darkly (1 Corinthians 13.12). Yet,
what we see, we recognise as having some meaning, some pattern. The
glorious picture is a humancomprehensible incarnation of the vast
and inconceivable. The logic takes on a shape - becomes flesh - and
we behold its glory (John 1.14), all from the relationships between
the two rectangles and a sheet of A4. Their position and size show
where to put the next dot, where the next crumb of activity can add
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
(above) illustrate this feature, which is 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 within 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 also a feature 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 Corinthians 12.27); and
"God in Christ" (Romans 6.11) all reflect the selfsimilarity of the
persons of God and of us in Christ. And Jesus's words, "I am the
vine and you are the branches" (John 15.5), speak of our becoming
similar to him, contained in him, structurally part of him; of our
being him in the world, just as one 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.
Free will is also important. The chaos game needs you, each time
you place a dot, to make a random choice about which of the two
rectangles you are going to use. No matter where you start (your
first dot), your dots will eventually become part of the shape -
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
THE exercise does not work if you keep choosing the same
rectangle. Then there is no beauty, and the picture fails. It is
the chaotic activity that we have in love, with relations, with
neighbours, with ourselves, and with God - the whole community
around us - which creates the beauty. Life needs some chaos; we
need to keep all the balls in the air.
Experiencing the infinite may overwhelm 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: in a
place 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 yourself,
on the ecclesiastical fractal website: splat.co.nr/chaos
The Revd Adrian Low is Emeritus Professor of Computer
Education at Staffordshire University, and Assistant Curate of
Abbots Bromley, Blithfield, Colton, Colwich and Great Haywood in
the diocese of Lichfield.