The Garden that cannot exist and the math that grows it anyway.
On M.C. Escher, the Fibonacci sequence, and the garden that is always more than one thing at once.
There is a gate in one of my client’s garden in Putney, half-hidden by a Portuguese laurel that has been growing there far longer than anyone remembers. Through it, at the right angle in October light, you can see two gardens at once. It lasts about three seconds. Then you move, and only one remains.
I have been thinking about this while stuck in a sudden downpour between jobs on my inner London round.
The view from the wrong position
If you are familiar with Escher’s work, he spent his career in the places where what we know and what we see refuse to agree. His staircases ascend forever. His hands draw each other into existence. His birds become fish, become sky, become earth — without ever arriving at a final form. He was not, in any traditional sense, a nature artist. He was a man who had noticed that reality is not a fixed thing we observe from a neutral position. It is something we construct, continuously, from wherever we happen to be standing.
"We adore chaos because we love to produce order." — M.C. Escher.
A garden is an Escher drawing you walk into. From the house, it is a composition — designed, contained, a view. Step through the door, and it begins to rearrange itself. The path that seemed straight turns out to be slightly curved. The Acer tree that anchored the whole picture from the kitchen window is, from beneath, an entirely different tree: a different structure, a different relationship to the sky, a different quality of shade. Both are true. They coexist without contradiction, like his monks on the impossible staircase — ascending and descending simultaneously, neither wrong, neither the whole picture.
This is not an illusion. This is what a garden actually is.
What grows in spirals
Pick up a pine cone. Look at the base of it — the scales spiral outward in two directions at once, one set curving clockwise, one anticlockwise. Count them. The two numbers will almost certainly be consecutive terms in the Fibonacci sequence: 8 and 13, or 13 and 21. The same is true of a sunflower's seeds, a pineapple's eyes, the arrangement of leaves on a rose stem. Not by design. By efficiency — the most economical way a growing thing has found to pack itself toward light without blocking itself.
The Fibonacci sequence — 1, 1, 2, 3, 5, 8, 13, 21 — is the arithmetic of growth itself. Nature didn't plan it. Nature discovered it, the way water discovers the path of least resistance, over and over, across every growing thing on Earth.
This is why planting in groups of three, five, eight works — not because someone invented a rule, but because the eye has been recognising this proportion since long before there were gardens. It feels balanced without feeling symmetrical. It feels intentional without feeling imposed. It leaves room for what a garden actually needs to be, which is not a composition but a living argument — one that keeps revising itself, season by season, in directions nobody entirely planned.
Charles Jencks understood this well enough to build thirty acres around it in Dumfriesshire: a garden shaped by the mathematics of black holes and fractals, turf and steel making the argument that the geometry we discover is the same geometry nature was already using. It is the strangest serious place in British landscape design (which I’m planning to visit by the way), and the point of it is simple: a garden is where multiple realities are permitted to coexist without resolving.
What this means in my small Islington world
Most of the gardens I work with are not thirty acres. They are thirty square metres, with a shared fence, a drainage problem and a neighbour's tree that changes everything about the light during the summer months.
I think about this often — what it means to create a garden knowing it will become something you didn't fully design. That the plants will make decisions. That something will self-seed in a position you'd never have chosen, and in year three it will be the thing that holds the whole middle distance together, and you maybe will stand there in October, slightly baffled, and take no credit for it.
Is that the whole point?
I'm genuinely not sure. But I know that the gardens I find myself returning to — the ones that stay with me — are never the ones that looked exactly as planned. They are the ones that, at the right angle, in the right light, for about three seconds, seemed to be two things at once.
And I know that is not a problem to be solved.
