Colour Science & Perception
what the eye settles, and what it cannot
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The thread: Say which colour — page 10

A swatch is a set of coordinates in a space, under an observer, on a display with a gamut. Every colour drawn here carries all four, because a hex code on its own does not identify a colour at all.
A lighter ink swings the residue through nought. For a five-per-cent tint on brightened office paper, printed instead with the same pigment diluted to a share of its strength over more of the paper — matched in colour on a non-fluorescent sheet — the hue turn a reader fully adapted to the sheet still sees, signed, against the dilution. The orange's -7.2° at full strength passes nought near 0.54 and reaches 10.3° at a quarter. What the brain does

A light ink can cancel the glow at one strength

A pale tint on brightened paper keeps a hue turn a reader fully adapted to the sheet cannot remove, and nine tenths of it survives every screen, because it is the tint's bare paper glowing beside ink that puts the glow out. A light ink — the same pigment diluted, printed over more of the paper — was the proposed lever, and the prediction that a quarter-strength ink lowers a five-per-cent orange's residue by a third. It does not lower it; it reverses it, from −7.2 degrees to +10.2. Somewhere between, the residue passes through nought, and for every one of eight pigments there is a strength that cancels it: 0.41 for the red, 0.54 for the orange, 0.80 for the blue and the cyan at a five-per-cent tint. The cancelling strength moves by under a tenth from five per cent to forty, so one ink per pigment keeps every pale tint within a degree and a quarter to twenty per cent, where full-strength ink leaves up to nine. The lever is real; it has a setting, and the light inks printers carry are diluted past it.

 Shared nodes fail the colours that bind below them and beat their own for the rest. For every strategy and cap on both rays, how much of the hard-cap gain its own three placed nodes buy the shared placement keeps — three nodes one, two and three units below the median binding point, L* 19.4 to 17.4 — against how far above those nodes the case's cap binds. Cases binding below them keep almost none; cases binding more than two units above keep more than all, up to 395 per cent. What it takes to deliver it

Shared nodes belong in the deep shadow

Three nodes placed just below where each dark colour's ink reaches the press's cap cut a four-ink table's dulling of that colour by a third — but a profile's nodes along lightness are shared by every colour, and the colours' caps bind anywhere from L* 15 to 31. The prediction was that one shared placement keeps two thirds of the own-placement gain on a deep-blue ray and all of it on a brown. Placed once, one to three units below the median binding point, the nodes keep 63 per cent of the blue's hard-cap gain and 92 of the brown's — and the averages hide a split. Every colour whose cap binds more than two and a half units below the shared nodes keeps under a twentieth of its own gain; every colour whose cap binds more than two units above them keeps more than all of it, up to four times. For those colours most of the dulling was never at the cap's corner: it lies in the deep shadow, where black keeps climbing under the cap, and the shared nodes sit there. Spreading the three nodes across the binding points buys nothing three even nodes would not.

 Every box's verdict, in length and width. Every solved box with its floor two to four units long, placed by its shorter and longer sides and marked by its verdict: all seventy-two paints gaining chroma under the satin finish, or all losing. The losses form a wedge that narrows from 0.35 to 0.5 at two units to 0.4 alone at two and a half, and is gone by three. What a scene does

The window of loss closes from both ends

A satin finish on a room's grey faces costs a painted floor a little chroma only in narrow rooms near square, and a floor two units long loses it only in a window of shorter sides, from about 0.30 to 0.51, while a floor three units long never does. The prediction for the floor two and a half units long was that the window closes from below: a gain at a shorter side of 0.3 and a loss only near 0.4 to 0.5, because the lower edge is where the far walls' pipe is weakest. The floor gains at 0.3, loses at 0.4 — by under six thousandths of a per cent — and gains again at 0.5. The window closes from both ends at once, to 0.39–0.42, and its deepest point rises through nought near 2.6 units long. Every box is still all or nothing, every one of seventy-two paints with the same verdict, and every verdict has the sign of the finish's tilt across the floor's reflectance. The far walls' cost shrinks smoothly with their distance and centres on a shorter side of about 0.4.

 One ink overshoots on the light sheet and falls short on the premium. Every pigment printed at the strength that cancels its ten-per-cent residue on the office sheet, its coverage matched to each sheet's own five-per-cent target: the residue a reader adapted to each sheet still sees, signed. On the office sheet it is near nought; on the light sheet seven of eight pigments' residues have turned past nought the other way, and on the premium sheet all eight keep the full-strength ink's sign, by under 1.8 degrees. What the brain does

One light ink serves three papers within two degrees

On brightened office paper a pale tint keeps a hue turn even for a reader fully adapted to the sheet, and each pigment has one light-ink strength — the pigment diluted and printed over more of the paper — at which that residue vanishes. The prediction for a printer with several stocks was that the cancelling strength falls as the brightener loading rises, and that the office sheet's ink leaves a premium sheet's pale tints within two degrees and a lightly brightened sheet's within one. The strength does fall, at every step and for every pigment — by a fifth for the orange and the yellow, by under one per cent for the green. The office ink keeps the premium sheet within 1.8 degrees, as predicted, but the light sheet only within 1.8 too: it overshoots there, turning seven of eight pigments' residues past nought the other way, and falls short on the premium sheet for all eight. Either way it removes more than four fifths of what the full-strength ink leaves.

 The fresh sheet's ink holds until half the brightener is gone. On the premium sheet as its brightener bleaches, the worst residue any of eight pigments leaves from five to twenty per cent: printed at full strength, with the fresh premium sheet's light inks, and with the office sheet's. The fresh premium inks stay under two degrees to half bleached (25%: 1.75°, 50%: 1.80°, 75%: 2.35°); the office inks, 1.80° on the fresh sheet, stay under one and a half once any of the brightener has bleached. What the brain does

An ink for a fading sheet is set for its middle age

A light ink cancels a pale tint's residual hue turn on brightened paper at a strength that falls along a straight line in the sheet's glow, and a brightener bleaches with use, so a sheet's glow falls over its life. The prediction was that as the premium sheet's brightener bleaches, every pigment's cancelling strength rises back along that line, and that the fresh sheet's ink stays within two degrees until half the brightener is gone. Both hold. Bleached by a quarter, a half and three quarters, the premium sheet asks for strengths within 0.015 of the census line at its glow, always on or just below it; the fresh premium ink errs by 1.75, 1.80 and 2.35 degrees at worst. But the office sheet's ink, set for a glow the premium sheet passes through on its way down, keeps the bleaching sheet within 1.4 degrees at every stage after the first. An ink set for the sheet's middle age outlasts one set for its first day.

 The turn is set by the level the blue arrives at. For displays with a red line at 630 nm, a green at 505 to 545 nm and the census's blues, balanced to D65: the turn — the blue at which adding green moves ICtCp's red–green axis from M-ward to L-ward — against the level the blue is delivered at, whatever peak and drive deliver it. With the 530 nm green it runs from 451.6 nm at 10,000 cd/m² to 457.3 at 10; a dimmer blue turns at a longer wavelength for every green. Matching and measuring

A tone-mapped blue turns where it lands

In ΔEITP a display's blue corner, and the turn at which adding green to it changes which side of ICtCp's red–green axis it moves the colour to, both shift with the display's peak, because the quantiser reads absolute levels. A high-dynamic-range picture graded on a bright master and shown on a dimmer panel is tone-mapped, its blues delivered below the levels they were graded at. The prediction was that a blue at a tenth of full drive on a 1,000 cd/m² panel turns where a 100 cd/m² panel's full blue does, and that the corner's move differs, because the dimmed blue no longer sits at a vertex. The turn agrees within a hundredth of a nanometre. So does the corner, within half a per cent: the steps both are read from are directions at one absolute signal, whatever drive delivered it. The tone map's whole effect on the blue is where it puts the blue. Through ITU-R BT.2390's curve, a master's bright blues are gathered near a dim display's peak and share one turn there — two nanometres from where the master turned them — while blues under the curve's knee keep their turns exactly.

 Per channel, a tone curve turns a sky's blue towards cyan. A blue of the 530 nm green's display mixed with a share of green, graded at full blue drive on a 1,000 cd/m² master and shown on displays of 100 and 300 cd/m² through BT.2390's curve applied to each channel or to the largest with all three scaled together: the change in the mixture's ICtCp hue from the master's. Per channel on the 100 cd/m² display the hue turns 23.4° towards the green at a tenth of green; scaled, it moves under three degrees at every share. Matching and measuring

A tone curve per channel turns a sky towards cyan

A pure blue tone-mapped from a bright master to a dim display turns, in ΔEITP, wherever its delivered level puts it, and any tone curve that delivers it to the same level gives it the same turn. A picture's blue is not pure. The prediction for a blue mixed with a little green was that a tone curve applied to each channel separately raises the green's share by about half — the blue channel compressed above the curve's knee, the dimmer green left near it — turning the mixture's hue several degrees towards cyan and its turn a nanometre or more from where a curve that scales all three channels together puts it. The turn does move, by 1.6 to 3 nanometres on a 100 cd/m² display and up to 6.5 on a 300. But the share is not raised by half: through BT.2390 to a 100 cd/m² display, a blue graded with a tenth of green arrives with its green at 69 per cent of its blue, nearly seven times as much, and its ICtCp hue turns 23 degrees towards the green. The scaled curve keeps every mixture's hue within three degrees and its turn within half a nanometre of the pure blue's.

 Easing the cap below L* 20 halves the dulling and more. For every strategy and cap on the deep-blue and brown rays, hard and through the fifteen-unit knee, the mean chroma a 65-node four-ink table loses below the cap with the cap held and eased by a tenth and a fifth on a straight ramp from L* 20 to the floor. Eased by a fifth the blue's hard-cap dulling falls from 9.71 to 4.89 thousandths and the brown's from 9.70 to 1.30. What it takes to deliver it

Easing the cap reaches the deep shadow and no higher

A four-ink table prints dark saturated colours duller than asked between its nodes, and for colours whose ink reaches the press's total-ink cap high up the dulling lies mostly in the deep shadow below L* 20, where black climbs under a held total. The proposal was to let the total fall below the cap there, and the prediction was that easing the cap by a tenth or a fifth between L* 20 and the floor halves those colours' dulling on even nodes — more than three shared nodes do — at a cost of a unit or two of L* in the darkest colour the press can reach. There is no cost: every eased table still prints the floor at L* 14. Eased by a fifth, the deep-blue ray's dulling halves and the brown's falls to an eighth. But the eight colours that bind above L* 26 keep three fifths of theirs: the ease removes two thirds of their deep-shadow dulling and none of what lies between their binding point and L* 20. And the eased cap does not let black rise less steeply — it makes black rise faster.

 For the high binders a higher ramp trades one stretch for the other. For the eight cases binding above L 26, the mean hard-cap dulling below L 20, between the binding point and L 20, and over both, against where the ramp starts. From L 26 the upper stretch falls from 6.18 to 2.31 thousandths and the deep shadow rises from 3.85 to 9.33: the total stays at 5.20. What it takes to deliver it

A higher ramp trades one shadow for another

Easing a four-ink table's total-ink cap by a fifth on a ramp from L* 20 to the floor halves the dulling of dark colours whose cap binds low, and leaves the colours that bind high with three fifths of theirs, because most of what is left lies between their binding point and L* 20, above the ramp. The prediction was that a ramp starting at L* 32 halves the high binders' dulling, at a small cost to the low binders. It does neither. Started at L* 26, the same fifth's ease does cut the high binders' upper dulling by more than half — the cap was its cause after all — but their deep-shadow dulling comes back to more than twice what the L* 20 ramp left, and their total is unchanged at 0.0052. The low binders give back nearly everything: on the brown ray from almost nothing to 0.0084 with the ramp at L* 32. Every ray, knee and group does best, or within a fiftieth of best, with the ramp at L* 20.

 Scaled by the height, the two rooms close their windows together. The deepest change in the painted floor's chroma over each length's solved shorter sides, against the floor's length over the room's height, for boxes 2.5 and 4 units tall. The 2.5-tall box's dip crosses nought at 2.59 units, 1.04 times its height; the 4-tall box's at 4.04, 1.01 times. What a scene does

A taller room keeps its floor losing in proportion

A satin finish on a room's grey faces nearly always adds a little colour to a painted floor, and in a box 2.5 units tall it takes some away only in a pocket of proportions: floors shorter than about 2.6 units, with a shorter side near 0.4. The prediction was that the pocket scales with the room's height — that a box four units tall keeps losing until its floor is about 4.2 units long, 1.04 times its height as in the lower box. It loses until 4.04 units, 1.01 times its height: the crossing scales, a little short of the prediction. The pocket moves too. At a shorter side of 0.4, where the lower box lost, the taller box's floor gains at every length; its losses sit at 0.6 — at three and four units long — and at 0.8 when three units long, and its deepest loss lies near a sixth of its height, as the lower box's did. Every box is still all or nothing across seventy-two paints, and every box's change carries the sign of its finish's tilt across reflectance.

 A sixth gained above L* 20, most of the cure lost below it. For the eight cases binding above L 26, the dulling below L 20 and between the binding point and L* 20, with the cap held, eased straight and eased on the bent ramp. The bent ramp cuts the upper stretch from 6.18 to 5.20 thousandths and raises the deep shadow from 3.85 to 7.16. What it takes to deliver it

A bent ramp takes more ink and dulls more

Easing a four-ink table's total-ink cap by a fifth on a straight ramp from L* 20 to the floor straightens the deep shadow's bend and halves the dulling of dark colours, and a ramp started higher trades the deep shadow's cure for the upper stretch's. The prediction for a ramp bent at L* 20 — a quarter of the ease spent between L* 32 and 20, the rest below — was that it keeps nearly all of the deep shadow's cure while taking a third off the high-binding colours' upper stretch, their total falling by a fifth. The bent ramp takes at least as much ink as the straight one at every lightness. It dulls every group more. The high binders' upper stretch improves by a sixth; their deep shadow loses half its cure, and their total rises from 0.0052 to 0.0060; the brown's low binders, left with almost nothing by the straight ramp, keep 0.0039. The deep shadow's cure follows how steeply the cap falls below L* 20 — a fifth of the cap over six units, not three twentieths — and not how much ink is taken there.

 Two rooms' floors as long as the room is tall, read as one row. The mean change in the painted floor's chroma over seventy-two paints under a satin finish, against the floor's shorter side as a share of the room's height, for the floor four units long in the box four units tall and two and a half long in the box 2.5 tall. Where the two rooms were solved at the same proportions their points coincide. Read together the floor loses from 0.148 to 0.176 of the height, the dashed lines; the deepest loss is 0.0056% at 0.16. What a scene does

A room scaled whole loses its floor to the last digit

A satin finish on a room's grey faces costs a painted floor a little of its chroma only in a pocket of proportions, and a box four units tall was found losing in proportion to a box 2.5 tall — its crossing at 1.01 times its height against the lower box's 1.04, its pocket near a sixth of the height in both. The prediction was that the answer is the room's proportions alone: that the four-tall box built as the 2.5-tall box multiplied by 1.6 gives the lower box's loss to the solver's precision, and that the floor four units long loses from about 0.55 to 0.65 wide. The scaled box gives the lower box's numbers to eleven significant figures, and a pair the census had already solved agrees to twelve. The window sits higher than predicted at both edges, from 0.59 to 0.70. And the gap between the two rooms' crossings was the census's sampling: read at the pocket, the taller room crosses at 1.029 times its height against 1.036.

 A narrower flank keeps most of the Lorentzian's losses. The forty-nanometre band pigment with its steep side fourteen, ten, seven and five nanometres wide at half depth: how many of the clear mercury lamp's 25 splitting directions it loses by more than one per cent, as a Gaussian and as a pseudo-Voigt with a twentieth of Lorentzian, beside the counts predicted. The Gaussian loses 4, 0, 0, 0; the Voigt 18, 13, 12, 7, where four were predicted at seven nanometres and none at five. Where the model breaks

A narrower flank moves its wing in with it

Under a clear mercury lamp, a band pigment whose steep side is a Gaussian fourteen nanometres wide loses four of the twenty-five directions that split the green line from the yellow, and with a twentieth of Lorentzian in that side it loses eighteen, because the wing three half-widths out out-absorbs the whole Gaussian there. A Lorentzian wing falls as the square of the distance over its half-width, and the prediction was that narrowing the side to seven nanometres brings the twentieth-Lorentzian pigment back to four losses and to five nanometres to none. It loses thirteen at ten nanometres, twelve at seven and seven at five, while the Gaussian loses nothing at all three. The wing still decides: the narrower band does not stay where the wider one sat but moves fourteen nanometres in towards the line it must pass, so its wing there falls fourfold rather than eightfold.

 The census line is a chord across a curve. For four pigments, the cancelling strength less the census line's at each sheet's glow — the light, office and premium sheets and the three bleached and yellowed premium sheets — in order of glow. The light and premium sheets sit above their own line and the office sheet under it, the orange by −0.0161, deeper than any bleached sheet: the line through the three census sheets is a chord across a sagging curve, and the bleached sheets sag beneath it as the office sheet does. What the brain does

A yellowing base leaves the ink where the glow put it

A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and as a premium sheet's brightener bleaches that strength rises back along the straight line in glow through three census sheets — a shade under it, by up to 0.013. Real photo-ageing yellows the base paper as well, and the prediction was that a base yellowed in step lifts the strengths onto the line within 0.01 and that the office sheet's ink still holds every residue within one and a half degrees. The ink holds, at 1.38°, 1.13° and 1.38°. The strengths do not lift: no pigment's moves by more than 0.0023, and its gap under the line by more than 0.0006. The yellowing raises the sheet's b* by 0.31 at most while the bleaching raises it by five. And the gap was never the base's: the office sheet itself sits 0.016 under the line, deeper than any bleached sheet. The line is a chord across a sagging curve.

 Per channel, a tenth of green lands where a half was graded. Each mixture's CIECAM16 hue quadrature on the master and through the per-channel curve, between unique green at 200 and unique blue at 300. On the master a tenth of green sits at 312.9 and a half at 277.5; per channel on the 100 cd/m² display the tenth lands at 260.9, past the master's half. Matching and measuring

An appearance model sees the per-channel sky turn twice as far

BT.2390's tone curve, applied to each channel of a 1,000 cd/m² master shown on a 100 cd/m² display, raises a sky-blue's green share from a tenth to 69 per cent of its blue and turns its ICtCp hue 23°, where the same curve applied to the largest channel with all three scaled keeps the hue within 3°. ICtCp's hue is not an appearance, and the prediction was that CIECAM16, read under the display's own white, still shows the per-channel turn as more than twenty hue-quadrature units and more than ten ΔEITP, the scaled curve under three of each. The appearance model sees it as fifty-two units, more than half the way from unique blue to unique green, and its lightness more than doubles. The scaled curve keeps hue and lightness to a quarter of a unit. And ΔEITP between master and display ranks the two curves backwards: in absolute light the per-channel sky is the nearer one.

 A blue's intensity sits below where the curve compresses. BT.2390's curve from the 1,000 cd/m² master to displays of 100 and 300 cd/m², with the level a pure blue, a tenth-green and a half-green sky present to it when the curve is applied to ICtCp intensity, and the level their blue channel presents when it is applied per channel or to the largest channel. The skies' intensity corresponds to 79 to 387 cd/m², against knees of 27.9 and 161.4; their blue channel sits at 1,000, the top of the curve. Matching and measuring

A curve on intensity cannot see a blue's brightness

ITU-R BT.2390's tone curve applied to each channel of a bright master turns a tone-mapped sky's appearance fifty-two hue-quadrature units towards green on a 100 cd/m² display; applied to the largest channel with all three scaled, it keeps hue and lightness to a quarter of a unit. BT.2390 also describes applying the curve to ICtCp's intensity and scaling its chroma, which keeps ICtCp's hue by construction, and the prediction was that it keeps the appearance's hue within three units and its lightness within two. It keeps the hue, within 2.3 units. It cannot keep anything on the display: a saturated blue's intensity is the PQ level of 79 cd/m², under the 300 cd/m² display's knee, so the curve barely touches it and every sky asks for two to seven times the blue the display has. Clipped channel by channel, the sky turns as far as the per-channel curve turned it; scaled back into the gamut, it lands where the scaled curve put it. The step back into the gamut decides the appearance, not the curve.

 Every stock's ink lies on the premium stock's curve. Five pigments' cancelling strengths at a ten-per-cent target against the sheet's glow: the premium stock at eleven brightener loadings from a tenth of its own to all of it, the light, office and premium census sheets, and the premium stock bleached until its glow equals the office's and the light's. Every census sheet lies on the premium stock's curve, and the bleached premium sheets on the census sheets — the orange at 0.5581 and 0.6461 against 0.5578 and 0.6456. What the brain does

The glow alone sets the light ink

A light ink cancels a pale tint's residual hue turn on brightened paper at one strength for each pigment, and that strength falls with the share of the sheet's luminance that is glow — along a curve, not the straight line through three census stocks, which runs as much as 0.016 above it. The prediction was that the strength is one curve in the glow whatever the stock: that a premium sheet bleached until its glow equals the office sheet's, or the light sheet's, needs that sheet's ink within 0.003 for every pigment. It needs it within 0.0007, though the two papers differ in base, in whiteness and in how much of the brightener their ink shields. Traced across eleven loadings of the premium stock, the curve runs through every census sheet within 0.003, sags under every chord, and falls five to nine times as steeply on a dim sheet as on a bright one for the orange, red and violet.

 The wedge of loss comes to a point at 1.04 times the height. Every box of the 2.5-tall room near the wedge, by its floor's sides as shares of the height, marked by whether every one of the seventy-two paints gains, every one loses, or they split, with the crossing along the row at 0.16 of the height. The floors 1.08 and 1.12 times the height long gain at 0.15, 0.16 and 0.17; the floor 1.04 times as long gains at 0.15 and 0.17 and splits at 0.16, 55 paints gaining; the row crosses nought at 1.0399. What a scene does

The wedge of loss comes to a point

A satin finish on a room's grey walls and ceiling adds colour to a painted floor in almost every proportion of room, and costs it a few thousandths of a per cent of its chroma in one narrow wedge of proportions: floors about as long as the room is tall and a sixth of its height wide. The wedge was known to close between floors 1.0 and 1.2 times the height long. The prediction was that a floor 1.04 times the height long still loses at a sixth of the height and one 1.08 times as long gains at every width near it, placing the tip between them a little above the coarse crossing of 1.036. The longer floor gains everywhere, as predicted. The 1.04 floor sits on the tip itself: its change in chroma is two parts in ten million, the row crosses nought at 1.0399, and there — and in no other box of the census — the seventy-two paints part company, fifty-five gaining and seventeen losing.

 Every paint has its own tip, and the pale ones cross last. Each of the seventy-two paints' own crossing from loss to gain along a sixth of the height, against how far its change swings between 1.0 and 1.08 times the height relative to the mean's, by band width. The crossings run from 1.0387 to 1.0413 of the height; the swings from ×0.37 to ×3.12, and the paints that swing most cross last. What a scene does

The pale paints cross the tip last

A satin finish on a room's grey faces costs a painted floor its chroma only in a narrow wedge of proportions, and at the wedge's tip — a floor 1.04 times the room's height long and a sixth of it wide — the mean change is nought and, alone in the census, the seventy-two paints part company: seventeen lose, fifty-five gain. The prediction was that the losers are the paints with the narrowest reflectance bands, whose chroma depends most on how much grey light mixes in, and that they lose most below the tip and gain least above it. The opposite holds. No narrow band loses; half the broadest do, and fourteen of the seventeen have the highest peak — the pale paints. They lose most below the tip and gain most above it: they are the paints the finish moves most, up to three times the mean, and each paint has its own tip, from 1.0387 to 1.0413 times the height, the palest last.

 A five-nanometre flank loses nothing up to a fiftieth of Lorentzian. The forty-nanometre band pigment's lost splitting directions against the Lorentzian share of its steep side, for a steep side five nanometres wide — the first search and the better of it and a second — and fourteen. At five nanometres: 0, 0, 0, 5 lost at no Lorentzian, a hundredth, a fiftieth and a twentieth, where the first search had 0, 0, 1, 7; at fourteen, 4, 11, 14, 18. Where the model breaks

A five-nanometre flank carries a fiftieth of Lorentzian

A band pigment splitting mercury's green and yellow lines with a steep side five nanometres wide loses none of the twenty-five splitting directions as a Gaussian and seven with a twentieth of Lorentzian in its flank, because the band slides in towards the passed line and carries its wing there. The prediction was that at five nanometres the count follows the single band's error, which grows in proportion to the share: about two lost at a fiftieth and none at a hundredth. A hundredth loses none, as predicted. The first search lost one direction at a fiftieth — and searched again from the best pigments found at the neighbouring shares, that direction reaches within two thousandths of the ideal: a fiftieth loses none either. The same second search recovers two of the twentieth's seven, leaving five. A sharp enough flank tolerates a fiftieth of Lorentzian where a fourteen-nanometre one lost fourteen directions to it.

 The loss deepens to 0.16 and jumps to a gain a hundredth wider. The same row between 0.15 and 0.175 of the height. The loss deepens at every step from −0.0016% at 0.150 to −0.0056% at 0.160, turns to +0.0010% at 0.164, sits at +0.00004% at 0.168 and loses again, −0.00076%, at 0.175. What a scene does

The pocket has a step where its bottom should be

Along a floor as long as the room is tall, a satin finish on the grey faces costs the floor a few thousandths of a per cent of its chroma in a pocket around a sixth of the height wide, deepest at 0.16 of the height by three samples a hundredth of the height apart. The prediction was that boxes between those samples trace one smooth dip with its bottom between 0.39 and 0.41 units, every box from 0.375 to 0.425 losing. The loss does deepen smoothly, at every step from 0.375 to 0.40. Then, a hundredth of a unit wider, at 0.41, every one of the seventy-two paints gains; at 0.42 they split; at 0.4375 every paint loses again. The row changes sign three times in a tenth of a unit of width, and the one step from 0.40 to 0.41 rises three times as fast as the pocket falls. The finish's brightening, which the chroma change rides on, falls smoothly straight through. What the census has called the pocket's bottom is a step.

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