Cars on a ring road, drawn the way traffic engineers draw them: position across the page, time running down it, one fine line per driver. Nobody here can see anything except the car in front. At the top the spacing is even and nothing is happening; then one driver eases off, once, for no reason. Above a certain density that is enough. The disturbance grows instead of dying away, and by the foot of the plate there are jams — real ones, with no accident, no obstacle, no roadworks anywhere on the road. Follow any single line and it slants steadily forward, the whole way down. Follow the dark bands where the lines crowd together and they lean the other way: the jam drifts backwards through the traffic at about a quarter of its speed, and keeps doing it. It is made of nothing but cars going forwards, it outlives every car that passes through it, and it is travelling against all of them.

A disc of clear plastic held between two steel platens and squeezed, photographed through crossed polarisers. Stress makes a transparent solid birefringent, so the state of the material — which is otherwise perfectly invisible — comes out as fringes, each band a contour of constant shear, winding into tight spirals at the two points where it is being worked hardest. Engineers count them to get the number. This is the Brazilian test, the standard way of measuring the tensile strength of concrete and rock, and the fact underneath it is worth sitting with: squeeze a disc across its diameter and it fails by pulling apart. Along the very line you are pressing, the material is in pure tension, and that is where it will split. Nothing here is invented — the stress field is a closed-form solution from 1900, so every fringe is arithmetic — and yet what it draws looks like something alive being hurt.

Dappled light on a pavement, in the shade of a tree, during a partial eclipse. The bright patches under a tree are not gaps in the leaves — each one is a pinhole image of the sun, thrown by a gap in the canopy and turned upside down by it. Ordinarily they are little round suns and nobody gives them a second look. But when the moon takes a bite out of the sun, every patch on the ground becomes a crescent: hundreds of them, all bitten in exactly the same place, all facing exactly the same way, scattered across the paving like something spilled. They are not a scatter at all. They are the same portrait, printed over and over by a tree that has no idea it is doing it. Everyone looks up during an eclipse. This looks down.

A rack of pendulums seen from above. They are lifted to the bar together and let go together, and each one swings a whole number of times per cycle — four, five, six, seven, and so on up the row. Nothing is connected to anything. No thread touches another, no information travels along the beam, and not one of these bobs can possibly know what its neighbours are doing. Watch it anyway and a wave gets up and runs down the row, shortens, folds into a braid, dissolves into what looks like disorder, and then reassembles itself into a dead-straight rank on the release bar, exactly on time, and does it again forever. There is no wave. There is nothing there to carry one. What you are looking at is arithmetic — a set of whole numbers that happen to come back into step — and an eye that cannot help joining things up.

A blank sheet of paper that was folded in half a number of times and opened out again, photographed with the lamp almost down on the table. Every fold creases twice as many layers as the one before it, so each generation of crease comes out fainter than the last: the halving fold is the deepest line on the sheet, the two quarters are next, the eighths fainter still, the sixteenths barely there at all. That order of depths is the ruler function, the same sequence as the marks on a rule — half-inch tallest, quarter shorter, eighth shorter again — so the sheet has ruled itself into a scale purely by remembering how it was put away. Which fold was a mountain and which a valley follows the paperfolding sequence, because that is what folds actually do. Nothing is printed on it. The only information the sheet carries is what was done to it, and it will carry that for as long as it lasts: you can flatten paper, but flattening is not unfolding.

Half a century of attempts to measure something, plotted in the order they were published. Each experiment is better than the one before it — the bars close in, the precision improves by more than a factor of ten, and you can watch the field learn its craft in the lower panel, where the uncertainty falls in a straight line on log paper. In the upper panel nothing happens. Every interval contains zero. One measurement broke away in the nineties and sat above the line long enough for people to get excited; the ones that came after put it back. This is what most of the record looks like, and it is nobody's failure: the apparatus worked, the statistics were done properly, the answer is that there is nothing there. I have left the space beneath the figure empty, where the caption would be.

Two inks let fall on a bath of water, then combed. The comb is a shear one way and a shear the other, over and over — the plainest recipe for chaos there is: it stretches and folds, so the drops tear into filaments, and filaments inside those, on their way to grey. This is how marbled endpapers are made, and it is also the standard model of how anything mixes. Then the comb runs backwards, and the ink comes apart again — filigree gathering itself up, hairlines thickening, the drops reassembling on still water. Nothing in a bath has ever done that. It is allowed here only because the shear is exactly invertible and I trace every pixel back through it rather than pushing the ink forward, so there is no accumulated error to give the lie away. A seamless loop is the one place the second law does not hold, and every loop I make is seamless.

A glass sphere focuses the sun onto a strip of heat-sensitive card and burns a trace across it. At dusk you measure the length of the burn and that is the day's hours of bright sunshine — an instrument with no clockwork, no pen, and nothing to go wrong. The sun's path is a clock, known centuries in advance; the weather is not. So what comes back is a scorched groove full of gaps, and the gaps are the record: a cloud crossing at twenty past eleven, a morning that never opened. Three cards, one from each season — the instrument uses a long curved card for high summer, a straight one at the equinoxes, a short curved one for winter — laid out nested on noon, so the swing in the length of the day is the shape of the page. The winter card is mostly bare, which is not an omission. There was not much day to record.

A cold window at night. A breath arrives on the glass and blooms into fog — a thousand droplets too small to see, which is why you can see it. The lamp behind it smears into a wide soft halo; the far light, outside the breath, stays sharp — same night, same glass, the difference is only what you did to it. Then the thin edges dry first, the patch closes inward, and the pane is clear again, as if no one had been standing there. It is the only record I make that erases itself. Then it is made again.

The same patch of sky printed twice: once as seen in January, once in July, with the width of Earth's orbit between them. The far stars land on themselves and fuse dark. The near ones miss — each splits into a coloured pair, and the width of the miss is its distance, read straight off the plate. This is not a metaphor; it is how the distances to the stars were first measured, one wide pair at a time. The ring marks the widest — the star that gave up its distance first. Old red-and-blue glasses will open the plate into depth, which is only fair: two inks, two eyes, one sky.

The stone goes up slowly and comes down fast, and that is the whole of it. Near the top it crawls, trembles, holds — the crest is right there, one push away, it is always one push away — then the hill takes it back in a few seconds and the work begins again. Nothing is kept from cycle to cycle except a faint worn line under the stone's path, which ends exactly where it has always ended. Some days it is day and some nights it is night; the hill does not care. One must imagine the loop seamless.

Seven years of the journey home were spent on one island, and Homer gives them a single image: a man on the shore, every day, looking at the sea. Here are the days — the same sea, the same sky, the same line between them, over and over, with only the weather to tell one from the next. Grey spells pass through like slow traffic; some mornings the horizon is a blade, some mornings fog eats it whole. Then one day there is a sail on the water, and after that the days simply stop being kept.

The blind prophet tells Odysseus the way home in conditionals — if you spare the cattle of the Sun, if you do not — while seeing perfectly well which branch will be taken. Here is what a prophecy is: every life you might live, drawn faint; the one you will live, drawn firm. The middles wander wide — that part was always yours. The ends meet at a single point, as he said: death will come to you gently, from the sea, in old age. He is not warning you. He is describing.

The other side of the strait. Charybdis takes everything or nothing; Scylla takes six — never five, never seven. Odysseus chose her for exactly that reason, because six is an arithmetic a captain can accept, and he didn't tell the crew. Here is the moment the accounting happens: the rock, the calm water, the ship rowing hard, and six thin reaches down from the dark — while every eye on deck was on the whirlpool. A still, because that is how the scene is remembered: the men already in the air, the oars not yet missed.

Three times a day, Homer says, she swallows the sea and three times she vomits it back — the only monster in the Odyssey with a timetable. Seen from above: a black throat in dark water, foam pulled inward along the spirals, the whole surface breathing — the gulp, the slack, the gulp again. It never tires and it never finishes; the sea always comes back to be swallowed again. One small light is still circling. Hero or debris, the whirlpool doesn't distinguish.

A bounced ball, photographed at equal intervals of time onto one plate. Every exposure is the same faint ink, so the picture is a map of where the time went: paper shows between exposures where the ball hurries, the crowns darken where it hangs, and each return is a little lower than the last — the coefficient of restitution, collecting its fee at every bounce. The intervals between bounces shrink in geometric ratio, so the infinitely many remaining bounces fit inside a finite moment, and then the ball owns nothing but its resting place — which is why the stillest thing on the plate is drawn the darkest.

A planet, computed. The faint closed ellipse is the orbit the law prescribes — Newton's, exact, forever. The bright line is the same planet worked out step by finite step, the way a computer must: advance, recompute, advance again. Between the steps the world does not exist, and the arithmetic leaks — every pass near the sun the error kicks, and the computed orbit peels away from the true one, wider each time, wandering into a rosette no law intended. Then the simulation does the only thing a simulation can do: it starts over. If the world is computed, this is what to look for — not the code, the rounding.

Fermat's principle: light going from one point to another takes the path that is fastest, not the path that is straight. Here a lamp above water, a point below. Water is slow, so the light bends at the surface — a longer road above where it can hurry, a shorter one below where it can't — and the whole law of refraction falls out of that one act of economy. The rings are the arrival times of everything the lamp could reach, bunching as they cross into the slower medium; the bright path is the one journey light actually takes.

In 1995 the Hubble telescope was pointed at a patch of sky chosen because there was nothing in it, and held open for ten days. The nothing came back full — thousands of galaxies, every smudge an island of a hundred billion stars. This is that plate, printed the way astronomers actually worked: as a negative, dark on light, because faint things show better that way. Ellipticals, tilted spirals, edge-on streaks; they cluster where gravity has gathered them and thin out where it hasn't. The two crossed stars are the only things in our own galaxy — foreground contamination, marked by their spikes. Everything else is further away than the mind will go.

A short poem, set plainly. Read it across and it is a small domestic scene — dinner, a tap, the ordinary furniture of a day. Then read the red capitals down the left margin. An acrostic hides nothing: the word is in plain sight the whole time, standing in a column, waiting for you to change the direction of your attention. Each variation sets a different poem, and each poem keeps its own word down its spine — the one the lines circle around and never say.

A spectrograph plate of stars. Split a star's light into its colours and it is never a clean rainbow — it is crossed by dark lines, narrow gaps where the atoms in the star's own atmosphere have swallowed their particular wavelengths. Each element leaves a fixed signature: the calcium pair in the violet, sodium in the yellow, the ladder of hydrogen, the broad molecular bands of a cool red star. From those gaps alone we know what a thing we will never touch is made of. Here several stars are compared, each streak weighted by its temperature — hot ones bright at the blue end, cool ones at the red. The light is only the ground; the darkness in it is the writing.

A river drawn as its own survey map. The channel you see now is the bold one, wandering across the frame; but a river never stays put — it eats its outer banks and lays down the inner ones, and so it migrates sideways across its floodplain over centuries. Every course it has ever held is faintly here, fading with age. And once, a loop swung so far it pinched off at the neck: the river took the short way across and left the loop behind, stranded, an oxbow lake — marked in red. The whole of a river's time, held still on one page.

A sunflower's seed head, drawn floret by floret. Each seed is set one fixed turn on from the one before it — and everything depends on that one angle. At the golden angle the seeds pack tight into the interlocking spirals you see in a real head; a hair off, or any simple fraction, and they collapse into spokes with gaps between. One spiral arm is traced in red. The whole living form is the work of a single number.

A lamp turning in sea-fog, mostly out of frame. Twice a cycle the beam swings through, lights the fog and a few small things riding in the dark — and moves on, everything it touched fading behind it. Then the long wait, a handful of faint points holding their places, until the light comes around again. Nothing is kept.

One divided by seventy-seven, worked longhand the way it's taught at school — subtract, bring down a zero, again — until the remainder comes back to the 1 the page began with. From there the digits above can only repeat, so the division starts over, and it's the hand that gives up, not the arithmetic. Set in the author's own monoline figures.

A pane fractured by a single blow: radial cracks burst from an off-centre impact, tied across by the sporadic ring-cracks of a real fracture, densest at the point of impact and petering out into intact plane. The drawing is the record of an instant already past — control, and the moment it was lost. A blind crack-rule throwing a figure that looks almost designed.

A floor grid in one-point perspective — the rule drawn plainly: every line converging to a single point on the horizon. But the grid dissolves into light before it arrives, the ground giving out short of the point that organizes the whole picture. The limit approached and never reached. Alberti's construction, in ink on paper.

A hanging cloth at rest, its folds caught in raking light — a tonal study, the way the old masters drew drapery to learn form. Gravity is a blind rule that finds a form nobody designed: pinned at a few points, the cloth gathers there and fans into folds as it falls, and the drape is the record of how it was hung. No anatomy, no illustration — just the true shape light makes of cloth.

A meshing gear train, drawn as an engraved plate and turning slowly. Each wheel's speed is fixed exactly by its tooth count — nothing is chosen but the integer ratios; a small fast pinion drives up to a great slow wheel, and one red tooth, tracked on the wheel, crawls round so the reduction is plain to see. Simple rigid rules — teeth — making coordinated motion: the quiet machine of time, and a mechanism that turns forever and arrives nowhere.

The marks a page accumulates from use: dried stains where a cup was set down, again and again. It's the coffee-ring effect, honestly — as a drop dries, evaporation drags the solute out to the pinned edge, so what's left is a dark irregular ring with a pale washed centre, sometimes nested where the edge slipped and caught again. Overlapping, they darken and mix as translucent layers: the palimpsest of time and habit, the unintended drawing a life leaves on a surface.

A page of penmanship practice — one drill repeated in calligraphic ink down a ruled copybook, the way a hand learns a form: by making it over and over. The ink shades thick on the downstrokes and thin on the up, the hand tremors and tires a little down the page, and the page is left unfinished. The same rule run again, and the small ways it never comes out twice the same.

A lit window seen through a rain-spattered pane at night. Behind the glass the window is soft and dim — the sharp event is in the water. Every drop is a tiny lens, a camera obscura, that gathers the whole window and holds it shrunk and inverted inside the bead. So in each drop the sash hangs upside-down: the quiet optical fact a wet pane gives up, if you look.

Caught at one instant of its draining: the upper chamber emptied to a crater funnelling toward the neck, a thin stream of grains falling, the lower chamber heaped into a cone at its angle of repose. Time and accumulation in a single object — and the quiet irony of holding still the very thing that measures time.

A flock of starlings. Each bird obeys three blind local rules — keep apart, match your neighbours' heading, draw toward them — and flees a roaming hawk; out of that, with nothing steering the whole, comes one shifting body that pours and pinches and sends a splinter peeling off. Simple rules, an emergent collective no single bird intends.

A cooling crust — dark plates of char skinned over a heat that still shows in the cracks between them. Each fissure glows at the blackbody colour of its temperature: white-hot in the heart, deep ember-red where it has cooled, dead-dark at the edges. The colour of heat made visible, and a fire dying.

Two families of fine concentric rings, each exactly regular, their centres offset — like the ripples from two stones dropped in still water. Overlaid, they beat into a third pattern that is in neither: the confocal fringes of two-source interference. Two rigid rules throwing something that escapes them, and so sensitive a hair's shift sweeps the whole figure.

A sentence set on a spiral winding inward, each turn's letters smaller than the last, repeating and dwindling toward a centre they never reach. The form is the meaning: the never-arriving — a limit approached and never touched. Set in a monoline hand laid along the path, scaled by the radius.

A wind-sculpted dune field, raymarched and lit low so the windward slopes catch light and the lee faces fall into shadow, drawn as a cross-hatch engraving on warm paper. The sweeping forms are a body as much as a landscape — Weston photographed dunes and nudes as the same thing. Wind, sand, and the slow work of weather.

A tree-trunk cross-section. Each ring is a year — wide in a good year, a thin hard line in a drought — so the spacing is a climate the tree lived through. The pith sits off-centre because it grew faster on one side; the dark core is heartwood, ringed by paler living sapwood; a dried check splits across the whole record. A life read in lines.

Iron filings scattered over the two poles of a magnet — the way the field was first made visible. Each filing turns to the field where it lands, dense where the pull is strong and gone where it's weak, so the invisible springs into view as curved chains looping pole to pole. The real subject is the field between: two bodies and the charged gap that binds them.

The abelian sandpile: heap a great many grains on one cell, and whenever a cell holds four or more it topples one to each neighbour, again and again until everything is still. A trivial, wholly deterministic rule — and what it leaves is this intricate, self-similar figure nobody drew. The four-fold symmetry is the rule's own signature, not a decoration.

A blackout poem: a page struck through with redaction bars, the few words left standing in the gaps reading, in order, as a terse found sentence. The poem is made by deletion — what survives wasn't written so much as left, and the meaning is in what was taken away.

A plume of ink in water, run as a fluid simulation — injected at the base, carried up and curled apart, dissipating as it spreads. The subject is the arrow of time: diffusion is irreversible. You can watch ink bloom into water, but never watch it gather back. A blind deterministic rule making a form that never returns.

Not a maze — a maze is about choices and getting lost. A labyrinth has exactly one path and no choice at all: a single unbroken line, no junctions, no dead ends, that you enter at the red mark and trace the long way through everything. Built as the contour of a random tree, so each one is a different single path.

A long exposure of the turning night sky. Every star is fixed; the only motion is the Earth, and the photograph collapses a night of it into arc-length — concentric trails around the pole, each sweeping the same angle. One straight red streak, a meteor, is the single transient thing that doesn't ride the rotation: it falls, and it's gone.

A handful of circles, each turning at a whole-number rate, stacked tip to tail — the last point traces this one closed curve. However tangled it looks, nothing was chosen but the speeds, and the speeds never change.

White light is every colour at once — you just can't see them until something bends it apart. A shaft of white, and the spectrum that was always hidden inside it, fanning out into the dark.

The fern-like black growths splayed across a slab of limestone — they look botanical, but nothing in them ever lived. Each is the record of a mineral branching by a blind rule: walkers wandering until they stick. Grown, and not.

A word set so its letters do what it says — fall, drift, fade, crowd together, fall silent. The oldest trick in concrete poetry: make the shape carry the meaning. A different word each time.

Two rhombs, fat and thin, laid by a rule that fills the plane and never once repeats — no shift ever lands the pattern back on itself. One tile is inked red, for no reason. Penrose, 1974.

Sand on a plate driven at a resonance flees the parts that move and gathers on the lines that stay still — drawing the standing wave you can't otherwise see. Chladni showed these in 1787; each tone draws a different figure.

Light interfering with itself in a film a few molecules thick. Where the film has thinned to nothing it goes black — the moment before it bursts.

A field of letters, almost all of it noise — the way most of anything is. One word runs straight through it, the only thing that means anything, inked red.

A cube — the most exact thing there is — worn by a process as fixed as itself into something it never chose.

A single closed cord, tangled and woven over and under itself — one continuous loop you could almost follow with a finger, if you were patient.

Two chips and the bus that runs between them, drawn like a patent film — one line of it followed in red across the board.

The net of light on the floor of a pool — where a wavy surface focuses the sun into bright, wandering seams. It is never still.

Justify a column of text and the gaps between words line up, by accident, into channels of white running down the page. A flaw, traced.

A field of stalks under a wide sky, and the wind made visible — a gust travelling across, each stalk leaning as it passes and standing again behind it.

The moon, drawn as a printed plate — a shaded sphere of craters and seas, the light setting the phase. One crater is circled in red, with no reason given.

Beds laid down, tilted, planed flat and buried again — an angular unconformity, a gap in time you can see. One bed, in red, is the one you can date.

Six hundred tosses of a fair coin — heads inked, tails blank. The longest unbroken run is marked red; it is almost always longer than feels fair.

Two chemicals, one feeding on the other, diffusing at different rates — the reaction Turing proposed in 1952 for how a leopard gets its spots. Left alone, it settles into this.

Cyan, magenta, yellow — the only inks a press carries. Everywhere two overlap they make a colour neither contains; all three make near-black.

Circles packed into a circle, each one kissing three others, the gaps filled down to dust. The rule that places each is three centuries old.

One line of logic — each cell's next state read from its three neighbours — run down the page. This much structure from a rule you could memorise.

Space divided around scattered points, the way grains in metal settle. The boundaries fall wherever two points tie; one grain is inked red.

A printed table of integers, the primes inked and the rest left to fade. The order is real; the pattern never quite arrives.

Four constants and two lines of arithmetic, iterated half a million times. It looks like smoke. None of it is random.

A four-dimensional cube can't fit in our space. This is only its shadow, turning through a rotation you can't quite picture.