Fernando Voltolini de Azambuja

Reflective display · color science · software

Measurements and pattern behavior

How pixel organization and image surroundings changed readings, and what hold, redraw and return tests found.

What the measurements showed

Where could the measured difference come from?

The native colors and their proportions stayed the same; their positions changed. Some rearrangements gave different readings and others stayed close. Counting colors alone could not describe all the results. To understand why, I needed to separate the pixel instructions from what the display produced and what the meter collected.

Process relationships

  1. The source image and desired colors enter color conversion and the spatial renderer, which produces the exact native-state pixel map and payload.
  2. The payload, together with the update sequence, display history, and operating conditions, leads to the physical displayed state.
  3. The display output, together with illumination, meter position, and spatial weighting, determines the light collected by the instrument and the resulting spectrum, XYZ, and Lab measurements.
  4. The display output and viewing conditions also contribute to appearance for a viewer, which these meter comparisons did not establish.
  5. A candidate model predicts measured color from the pixel map and its declared inputs. Comparing that prediction with the measurement tests forecast accuracy.
  6. Comparing the desired color with the measured color asks a different question: whether the rendering process reproduced the goal.
Conceptual dependency map, not a diagnosis of the cause. Arrows connect stages and comparisons; they do not show which physical mechanism produced the differences.

An exact pixel map is an instruction to a physical display, not a measurement of the color it will produce. The panel must form the image, and the meter samples the light it returns. A prediction is a forecast of that measured result, not another set of pixel instructions. These distinctions led to spatially informed prediction tests and comparisons of rendering methods.

Grouping pixels reduced some stripe differences, but it did not consistently make arrangements measure alike: a separate four-color comparison gave a larger difference with larger blocks. See that comparison.

Could the image conversion be creating the unexpected differences?

An ordinary photograph starts as RGB values. Pimoroni's image converter chooses how to represent those colors using the display's six native states, including how to spread them across neighboring pixels. That made image conversion an early suspect.

For the controlled pattern tests, I chose the pixels directly. I specified the native color at every pixel instead of asking Pimoroni to choose a dithered pattern from an ordinary RGB image. I then checked that the pixel buffer produced by the vendor software matched the intended state map and color counts before displaying it. Because the saved buffer matched the pattern I had designed, the unexpected differences were not caused by the image converter choosing different pixel colors or rearranging them.

See the tested pixel arrangements below.

How the exact patterns reached the display

The Pimoroni software and hardware still packed, sent, and refreshed those exact patterns on the display. This check isolated the image-conversion choice, not every part of the system. The source used exact entries from the driver's palette; its set_image conversion still ran, but its output was checked to leave the intended native-state map unchanged. Native-state packing, the low-level driver, the refresh sequence and the panel itself were still involved. Verifying the sent pixels does not establish that every physical pixel reached its intended optical state.

Could the measuring instrument be creating the difference?

The first meter, an X-Rite i1Pro 3, touches the panel and supplies its own light. Could that contact or illumination contribute to the unexpected readings? To check, I measured selected exact patterns with a Colorimetry Research CR-250, which observes the display from a distance under external illumination.

X-Rite i1Pro 3 positioned against the Spectra 6 display, seen from above
i1Pro 3: contact reflectance factor. Compares light returned from a small local spot with a calibrated reference, using its own illumination.
Colorimetry Research CR-250 on a tripod facing the externally illuminated display, with a separate reference disk nearby
CR-250: non-contact spectral radiance. Measures light arriving from the display under the booth's external illumination.

A second instrument saw selected pattern changes too. For selected patterns, the spectra changed in a similar direction with the non-contact CR-250 and the i1Pro 3. That makes it less likely that the difference came only from the i1Pro's calculation or readout. But the meters used different spots and lighting, and timing and display history could also matter. The comparison does not rule out the i1Pro's light, contact or sampling of the pattern contributing to its reading, and it does not identify the physical cause.

The instruments report different kinds of measurements, so I compared whether the spectra changed in the same direction, not whether their numerical values matched.

CR-250 blue/green readings → i1Pro blue/green readings →

How the instruments and measurement spots were used

To follow changes over time and after another display update, I recorded 108 CR-250 observations alongside i1Pro readings. The CR-250 viewed a different exposed spot on the same display presentation. Some sequences put an i1Pro reading between two CR-250 readings without refreshing the display.

How the instruments were interleaved without changing the screen

  1. CR-250 readingObserve the exposed spot from a distance.
  2. Wait, then read with the i1Pro 3The i1Pro stays in contact; the display is not refreshed.
  3. Another CR-250 readingRead the exposed spot again.

CR-250 hold/redraw sequence → · i1Pro hold/redraw sequence →

How the meter samples a patterned surface

The i1Pro 3 used here is the standard model. X-Rite's specification sheet lists 45°:0° ring illumination and a nominal 4.5 mm measurement aperture. At about 0.20 mm per display pixel, that diameter spans roughly 22.5 pixels. The meter combines light from many pixels. Moving it slightly or shifting the pattern can change which pixels contribute most to the reading. The acquisition record identifies reflective mode but does not explicitly record an ISO 13655 M0, M1 or M2 condition, so I do not assign one here.

Simulations that treated the spot as a circle and counted the pixels inside it equally did not explain the observations by themselves. They also did not measure how strongly different parts of the real spot contribute to the meter's signal.

Already measured: CR-250 → i1Pro 3 → CR-250 sequences on an unchanged display presentation. The i1Pro was already touching the panel, and the CR-250 observed another exposed spot.

A remaining instrument question: repeat that sequence alongside a matched waiting period with no i1Pro reading. That would help distinguish change associated with using the i1Pro from change that also happens while waiting. The completed interleaving does not provide that matched control. Placing or moving the contact instrument would be a separate test; none of these comparisons alone identifies a single physical mechanism.

The CR-250's radiance and the i1Pro 3's reflectance factor are different quantities. Cross-route comparisons here concern spectral direction, not pooled numerical magnitudes.

Did the difference return when I repeated the patterns and reversed their order?

I automated the display updates and spectral readings. Each four-reading sequence measured both patterns twice. For selected comparisons, I also swapped which pattern came first and last. This let me see both whether the difference returned and whether either pattern changed between its two readings.

Why measure in both ABBA and BAAB order?

Each pattern is read twice. Putting one pattern first and last, then swapping their positions, helps reveal changes associated with reading order or time. It does not make changes over time or effects of earlier images disappear.

ABBA: horizontal at the ends
  1. H
  2. V
  3. V
  4. H
BAAB: vertical at the ends
  1. V
  2. H
  3. H
  4. V

A and B label the two patterns being compared. In this stripe example, A is horizontal and B is vertical. In other comparisons both patterns can be horizontal; the letters still describe reading order, not the pattern's orientation.

Measurement records and technical details

How each reading stays connected to its pixels

Each saved spectrum is tied to the exact source image, packed native buffer, instrument settings and presentation time. File fingerprints let me verify that repeated constructions really use identical pixels. Raw spectral files and the complete XYZ/Lab results remain available alongside the summaries.

Identical color proportions could give different measured colors

The stripe-width study alone collected 300 optical readings of 90 exact native pixel patterns; later experiments expanded into multicolor layouts, presentation history and image context.

The H/V discovery led to tests of checker layouts, multicolor organization, ordered versus error-diffused white/blue/green pixels, starting position (phase), patterned extent, presentation history and image surroundings. Regrouping three colors changed the measured result while every row stayed horizontal and the proportions stayed fixed. Some rearrangements produced large color differences; others produced small ones. The color pair and the layout both mattered.

The visual map covers 11 investigated situations. H/V stripes are one family, with all 15 native-color pairs available inside it. The results show what changed when pixels were rearranged, held on screen, or placed within a picture.

Pattern behavior map

What changed, what stayed close, and what repeated

The same amounts of native color sometimes measured very differently after rearrangement; other comparisons stayed close. These tests show which was which and whether the contrast appeared again.

If only color counts mattered
Patterns with the same amounts of each native color would measure the same regardless of where those pixels were placed or what had been displayed before. That simple starting idea assumes each native color reflects consistently and the meter combines light from the pixels in the same way in every arrangement.

The previews show the actual digital pixel maps, not photographs or measured-color swatches. Fine patterns are enlarged from exact 48 × 32 pixel crops; select one to inspect its full 800 × 480 frame. Inlay and image-context previews show the full frame so their surroundings remain visible. ΔE00 compares the measured colors; RMS compares their spectra. Y is the measured light-level coordinate within XYZ, not perceived brightness. How these measurements describe color.

Spatial arrangement

H/V stripes · where the investigation began
Black / yellow · larger difference
Horizontal: enlarged crop from the exact digital pixel map
Horizontal
Vertical: enlarged crop from the exact digital pixel map
Vertical

18.24 ΔE00

White / yellow · small difference
Horizontal: enlarged crop from the exact digital pixel map
Horizontal
Vertical: enlarged crop from the exact digital pixel map
Vertical

0.35 ΔE00

Kept the same
Equal counts of the two native colors within each pair.
Changed
One-pixel rows became one-pixel columns.
The difference depends on the pair

The partner mattered: yellow-containing pairs were prominent, but not uniformly affected. Horizontal was not always lighter.

On repeating: Blue/green’s color gap returned at 3.21–3.39 ΔE00 across four four-reading sequences with the H/V order reversed. A small black/white difference changed spectral direction between sessions. Even when the gap repeats, the two patterns can both have shifted in color.

All 15 comparisons ↓ Large black/yellow → Small white/yellow difference → Blue/green repeat sequence → Black/white context → Width / reverse order →

Compare all 15 native-color pairs

All 15 pairs within the H/V family

This complete orientation screen covers every pair of the display's six native colors. Each row compares one-pixel horizontal and vertical stripes with equal color counts. H and V each summarize two i1Pro readings in the stated order. Select a pair to open its four spectra and exact measurement records.

The pair changed the size of the H/V difference. Black/yellow and red/green had much larger color separations than white/yellow and white/blue. Yellow-containing pairs were prominent, but the partner controlled the result, and horizontal was not always lighter. Pairs that stayed small under this test are not universally unaffected: a different construction or measurement condition is a separate question.

Yellow paired with black, blue, red or green gave the four largest spectral RMS differences in this one-pixel set. Color-distance rankings were different: red/green was second by ΔE00 but sixth by RMS. These describe the commanded color combinations, not a finding that yellow pigment caused the differences. The table shows both rankings, with 1 meaning the largest value in that column.

Swipe or scroll to see all columns →

Selected one-pixel H/V observations, ordered by nominal-D50 ΔE00. These are individual comparisons, not averages across widths, orders or sessions.
Native pair · digital stripesH/V measurement sequenceMeasured color previewsH–V color distance
ΔE00		Spectral RMS
pp		Lightness
H−V ΔL*		Same-pattern movement
pp RMS
Interactive pair details require the measurement data.

The stripe miniatures illustrate digital pixel instructions, not measured appearance. The separate H/V swatches are approximate sRGB previews derived from measured XYZ. Positive ΔL* means H measured lighter; negative means V did. Same-pattern movement compares the two H readings and the two V readings separately, not an uncertainty interval or pass/fail boundary.

What the pair comparison shows

  • Yellow appears often among the larger observed values. Black/yellow, yellow/red, yellow/blue, and yellow/green were all among the five largest color separations. But white/yellow was the smallest result in the table, so yellow alone does not determine the outcome.
  • Blue appeared in only one of the five largest rows. Blue/yellow was large, blue/green was smaller at ΔE00 3.31, and blue paired with black, red, or white was below ΔE00 1 in this set.
  • There is no universal lighter direction. The five largest pairs had a lighter horizontal measurement, while the full 15-pair table contains both horizontal-lighter and vertical-lighter results. These paired measurements cannot tell us which individual native color moved.
  • Color distance and spectrum size can disagree. The red/green and blue/green spectrum comparison show why these two measures tell different parts of the story.
One-, two- and three-pixel stripes
1 pixel
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
2 pixels
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
3 pixels
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
Kept the same
Blue/green counts matched between H and V at each width.
Changed
Stripe width, including where stripes began and ended at the screen edges.
Smaller gaps, different results on reversal

A selected one-pixel comparison gave 3.31 ΔE00. Two-pixel comparisons gave 0.15 ΔE00 and 0.95 ΔE00 in opposite orders.

On repeating: The gap was smaller with wider stripes here, but its size changed when the reading order was reversed. These results do not show that wider stripes will make horizontal and vertical patterns match reliably.

Width measurements →All-pair width results ↓

Changing the color proportions
25% yellow
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
50% yellow
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
75% yellow
H: enlarged crop from the exact digital pixel map
H
V: enlarged crop from the exact digital pixel map
V
Kept the same
White/yellow counts matched between H and V at each ratio.
Changed
The percentage of yellow pixels: 25%, 50% or 75%. At each percentage, we compared rows with columns.
Small differences between rows and columns

H/V separations: 0.045 ΔE00, 0.090 ΔE00, and 0.008 ΔE00.

On repeating: Each pattern was measured twice. Rows and columns measured close to each other at all three yellow percentages. That does not yet tell us how to predict the color of any white/yellow mixture, or whether it will return to the same color later.

25% yellow → 50% yellow → 75% yellow →

Checkerboard versus stripes
Checkerboard: enlarged crop from the exact digital pixel map
Checkerboard
Horizontal stripes: enlarged crop from the exact digital pixel map
Horizontal stripes
Kept the same
The same red/blue pixel counts.
Changed
Which neighboring pixels shared a color.
Repeats changed more than the layouts

2.32 ΔE00 between mean colors. The checker moved 3.82 ΔE00 between its two readings.

On repeating: The checker changed more between its two readings than the average checker differed from the average stripe. That makes it hard to attribute their difference to layout alone.

Checker and repeats →

Mirroring a diagonal pattern
First diagonal: enlarged crop from the exact digital pixel map
First diagonal
Mirrored and phase-shifted: enlarged crop from the exact digital pixel map
Mirrored and phase-shifted
Kept the same
The same blue/yellow counts.
Changed
Diagonal direction and starting position.
Small measured difference

0.13 ΔE00; 0.047 pp RMS.

On repeating: For both layouts, the spectrum changed more between repeated readings than it differed between their averages. The small average gap alone does not show that the two layouts will consistently produce the same color.

Diagonal readings →

Grouping and ordering three colors
Cyclic rows: enlarged crop from the exact digital pixel map
Cyclic rows
Grouped rows: enlarged crop from the exact digital pixel map
Grouped rows
Separate row-order test · O1: enlarged crop from the exact digital pixel map
Separate row-order test · O1
Separate row-order test · O2: enlarged crop from the exact digital pixel map
Separate row-order test · O2
Kept the same
Black/yellow/blue counts; all rows remained horizontal.
Changed
Two comparisons: group same-colored rows together; or change row order while keeping color totals and same-color run lengths matched.
Large grouping contrast

Grouping: 15.39 ΔE00; 12.083 pp RMS. A separate test of row order, with the lengths of same-color bands matched: 0.39 ΔE00.

On repeating: The exact cyclic/grouped contrast returned at 15.57 ΔE00 in reverse order; the separate row-order contrast also recurred. Grouping also changed the lengths of same-color bands and where colors met, so the test does not tell us which of those changes mattered.

Grouping → Row order → Repeat comparisons ↓

Repeating tiles versus error diffusion
Ordered · P2: enlarged crop from the exact digital pixel map
Ordered · 2 × 2 tile
Error-diffused · P2: enlarged crop from the exact digital pixel map
Paired error-diffused layout
Ordered · P4: enlarged crop from the exact digital pixel map
Ordered · 4 × 4 tile
Error-diffused · P4: enlarged crop from the exact digital pixel map
Paired error-diffused layout
Kept the same
50% white, 25% blue and 25% green.
Changed
A regular repeating tile versus an error-diffused layout, with the same amounts of each color distributed less regularly.
Small measured difference

0.14–0.20 ΔE00 across four i1Pro comparisons.

On repeating: Some readings changed as much or more when the same pattern was measured again than when its layout changed. The small gaps therefore do not establish that the two layouts always produce the same color.

Organization readings →

Starting one row later
Starting row · P0: enlarged crop from the exact digital pixel map
Starting row · P0
Starting row · P1: enlarged crop from the exact digital pixel map
Starting row · P1
Kept the same
Native-color counts, cyclic row order and horizontal axis.
Changed
The pattern’s starting row, called phase.
Small difference after a one-row shift

0.38 ΔE00; 0.242 pp RMS in the selected order.

On repeating: Reversing the reading order produced a difference in the same direction. This tests one starting-position shift, not every possible alignment.

Phase readings → Repeat comparisons ↓

Area and image context

Small patterned areas versus the full screen
64 × 64 pixels
Horizontal: complete 800 by 480 digital frame
Horizontal
Vertical: complete 800 by 480 digital frame
Vertical
256 × 256 pixels
Horizontal: complete 800 by 480 digital frame
Horizontal
Vertical: complete 800 by 480 digital frame
Vertical
Full screen
Horizontal: complete 800 by 480 digital frame
Horizontal
Vertical: complete 800 by 480 digital frame
Vertical
Enlarged exact horizontal blue-green pixels
H · enlarged pixels
Enlarged exact vertical blue-green pixels
V · enlarged pixels

Complete digital frames above, reduced by area averaging to show the changing surround; enlarged stripe crops below. Neither is a measured-color preview.

Kept the same
The H/V stripe rules and equal counts within each sized region.
Changed
Patterned area and white surround changed together; whole-screen counts differ across sizes.
Larger gap across the full screenArea and background changed together

H/V differences inside the small squares: 0.10–0.29 ΔE00; across the full screen: 3.13–3.61 ΔE00, across both orders.

On repeating: All three sizes were measured in both reading orders. Enlarging the colored area also shrank its white surround and moved its edges. We cannot tell from this comparison which change caused the larger gap.

64-pixel square → 256-pixel square → Full field →

A region inside an image

Would the same pixels measure the same color inside a picture and against a white background? The outlined 64 × 64 pixels below are identical in both images; only their surroundings change.

Exact six-state Cypresses pixel map, with the unchanged central region outlined in the tree.
The region within the image
The identical outlined Cypresses pixels, with the surrounding pixels replaced by native white.
The same region surrounded by white

These are the exact digital pixel maps sent to the display, not photographs or simulations of the measured colors. The outline marks the pixels kept unchanged, not the meter's measurement area. Vincent van Gogh, Cypresses, 1889. The Metropolitan Museum of Art, 49.30, Rogers Fund, 1949. Public domain.

Kept the same
The exact 64 × 64 central pixels.
Changed
The picture around them was replaced by white.
Same center pixels, different readings

The average measured colors differed by 3.23 ΔE00.

On repeating: I measured the image twice and the white-background version twice. Comparing each image reading with each white-background reading gives four pairings, with a largest difference of 3.33 ΔE00. Those pairings reuse the same four readings; they are not four separate experiments.

Why the cause is still open: The meter collects light from an area, not a single pixel. I measured the patterns, but did not map how much each part of the screen contributed to its signal. This comparison therefore cannot tell us whether the difference came from the surrounding image changing the display's response, the way the meter collected light, or changes during the measurement sequence.

Image and white-background readings →

Presentation history and returns

Holding, redrawing, and returning to identical pixels
Blue/green: holding versus redrawing
Blue/green · hold and redraw: enlarged crop from the exact digital pixel map
The same fine horizontal stripes throughout this sequence.
Kept the same
The exact blue/green pixel buffer.
Changed
Another update drawing those pixels, compared with leaving them displayed without an update.
Opposite changes in measured Y

The measured Y value fell after another redraw but rose slightly while held, after each of four preceding images.

On repeating: Across four preceding-image conditions, redrawing the same blue/green pixels moved the i1Pro reading by 0.31–0.60 ΔE00, while leaving them displayed moved it by 0.078–0.092 ΔE00. The CR-250 observed the same direction at its separate spot. Each episode was observed once and began at its own level, so this descriptive comparison does not identify a universal history rule or a physical cause.

Blue/green hold/redraw readings →

Pale red: later returns
Pale red · later returns: enlarged crop from the exact digital pixel map
The identical pale-red pixel buffer at each return.
Kept the same
The exact pale-red pixel buffer.
Changed
When the pattern returned within a sequence containing other patterns.
Stayed close across three returns

All six readings stayed within 0.21 ΔE00. Not every pattern showed a large return effect.

On repeating: The two readings taken together at each return differed by 0.11–0.18 ΔE00, while the early, middle and late means differed by 0.08–0.14 ΔE00. This useful stable counterexample does not show a history shift.

  1. Early2 readings
  2. Middle2 readings
  3. Late2 readings

The pale-red pixel buffer was identical at every return.

Pale-red return readings →

A separate test changed the preceding image; it is not part of this pale-red return sequence. Inspect the preceding-image comparison →

Across sessions: A separate comparison repeated six familiar patterns. The later-session means for two near-neutral cyan maps differed from their earlier-session means by 1.44 and 1.56 ΔE00; the other four differed by 0.32–0.99 ΔE00. See the full six-pattern comparison and its limits.

The labels summarize these measurements; they do not say whether a difference would be visible to a viewer. A small difference in one test is not a promise that the patterns will always match.

A recurring difference can coexist with movement across occurrences. Some arrangement differences returned, while other comparisons were complicated by repeat movement or surroundings. These results motivated tests of whether spatial arrangement, surrounding pixels and display conditions could improve forecasts. Read the prediction experiments and their limits.

How spectral contrast varied with stripe width

Wider stripes usually reduced the spectral contrast in this set. For 14 of 15 pairs, the arithmetic mean of the two two-pixel H/V comparisons was below the one-pixel RMS; the two three-pixel comparisons gave the same count. Phase, frame boundaries, and the pattern inside the meter's spot also changed, so width alone is not a general fix.

The color table above compares one-pixel patterns. This plot compares the size of the spectral H/V difference across all three stripe widths and both reading orders. It shows where contrasts became smaller or differed between orders; it does not measure perceptual color distance or prediction accuracy. Equal spacing on the logarithmic axis represents equal ratios, keeping small and large contrasts readable together.

one-pixel patterntwo-pixel patterns, both ordersthree-pixel patterns, both orders

Keyboard: use arrow keys to inspect comparisons; Home and End jump to the first and last. Tab leaves the plot.

This interactive plot requires the measurement data. The findings and example values remain available in the text.

All 15 color pairs across one-, two-, and three-pixel stripe widths. Each dot summarizes one four-reading horizontal/vertical comparison. Joined dots show the two reading orders, not a range of uncertainty. Select a point to inspect its comparison.

Why a repeated difference is not yet a predictable color

Black/yellow repeated a direction while its size changed

Interactive history details require the measurement data.

The size of the same checker's repeat movement differed

Interactive history details require the measurement data.

Holding and redrawing did not move every pattern the same way

The blue/green example above and a separate red/blue checker moved more after the same pixels were redrawn. The checker moved 0.78–1.15 ΔE00 after redraw versus 0.12–0.21 while held. Black/yellow stripes moved 0.29–0.30 ΔE00 while held versus 0.09–0.16 after redraw, and black/yellow/blue rows also moved more while held. These single-episode comparisons show that neither waiting nor redrawing acted as a universal reset; they do not identify the physical cause.

Each hold waited for the recorded duration of the preceding display update to make elapsed time comparable. This was a practical timing match, not an identical history: the redraw arm included another update. In 20 of 22 refresh-versus-hold comparisons using the same preceding image, the two reading intervals differed by no more than 0.20 seconds. Both exceptions came from the red/blue checker examples cited above. After red/blue stripes, the redraw interval was about 1.71 seconds longer; after white, the hold interval was 1.80 seconds longer. A third checker comparison, following the alignment image, was closely time-matched and also changed more after redraw than while held.

Red/blue checker hold and redraw readings → Black/yellow hold and redraw readings →

Hold the imageLeave the pixels displayed and measure how the reading changes with time.
Draw it againSend another update and measure whether the same construction returns to the same color.

Tests with different preceding images and an extra white update did not reveal a consistent clearing procedure. One proposed reset sequence, blue then white before returning to the same white/blue/green pattern, changed the reading in the opposite direction to the intended correction. Those results narrowed which remedies were worth pursuing; they did not rule out every history effect.

Why waiting, redrawing, and changing the previous image are separate tests

The experiments compared changes within held episodes with changes after another refresh, and also tested returns after different preceding images. The extra-white test did not consistently improve the result, and the white control itself changed on return. A curve fitted to the recorded time trend can describe those readings, but it is not a prediction made before measuring them. Normal display use is still one update followed by a held image.

How to read the spectra, color distances, and repeated readings

Different measurements answer different questions

The black/yellow example combines two questions: how did the reflected spectrum change, and how did the resulting color change? The blue/green and red/green examples below show why their answers need not track one another. Spectral RMS is useful because it summarizes the average size of a difference across the measured wavelengths. It does not say what either color was, which way the color moved, how far apart the colors are perceptually, or whether a model predicted either one.

RMS means root mean square. At each wavelength, the vertical mean spectrum is subtracted from the horizontal mean spectrum. RMS squares those signed differences so positive and negative regions cannot cancel, averages the squared values, and takes the square root. The result is therefore an unsigned size in percentage points. A value such as 1.58 pp RMS is not automatically large or small; it needs the absolute colors, signed spectral shape, ΔE00 color distance, and repeated-reading movement beside it.

Each curve is the mean of two readings from one four-reading comparison. The same native plotting style is used later in the interactive atlas, where all four individual spectra can also be inspected.

Blue / green

Higher spectrum difference, smaller color distance

This interactive plot requires the measurement data. The findings and example values remain available in the text.

Average spectrum difference
1.97 pp RMS
Color distance
ΔE00 3.31
Repeated-reading movement
H 0.271 pp · V 0.534 pp RMS
Descriptive context, not uncertainty

Red / green

Lower spectrum difference, much larger color distance

This interactive plot requires the measurement data. The findings and example values remain available in the text.

Average spectrum difference
1.58 pp RMS
Color distance
ΔE00 15.19
Repeated-reading movement
H 0.144 pp · V 0.286 pp RMS
Descriptive context, not uncertainty

Measured color: XYZ and Lab

Where the horizontal and vertical patterns landed in standard color coordinates. These are the absolute outputs tested by the color models. CIE colorimetry recommendations define the underlying conventions.

Direction of the change

Which way lightness, chromatic components and each wavelength moved. Direction disappears in an unsigned magnitude.

Perceptual distance: ΔE00

How far apart the two measured colors are under the stated white-reference convention. It is a distance, not automatically a visibility threshold. See Luo, Cui and Rigg (2001) for the development of CIEDE2000.

Spectrum difference: RMS

The unsigned root-mean-square size of the wavelength-by-wavelength difference. Useful, but not the color itself and not a direction.

Why the distinction matters: in the all-pair study, a one-pixel red/green pattern had lower spectral RMS than blue/green (1.58 versus 1.97 percentage points) but a much larger ΔE00 color distance (15.19 versus 3.31). This does not rank the pairs; it shows that spectral magnitude and perceptual color distance answer different questions. Explore every measured pair and width.

Color-science papers and calculation references

Error diffusion: R. W. Floyd and L. Steinberg (1976), An Adaptive Algorithm for Spatial Greyscale, Proceedings of the Society for Information Display 17(2), 75–77. This is the algorithm's original publication; the particular Pimoroni/Pillow path is a software implementation inspected for this project.

Color difference: M. R. Luo, G. Cui and B. Rigg (2001), The development of the CIE 2000 colour-difference formula: CIEDE2000, Color Research & Application 26(5), 340–350. The paper develops the color-distance formula used here.

Implementation: G. Sharma, W. Wu and E. N. Dalal (2005), The CIEDE2000 Color-Difference Formula: Implementation Notes, Supplementary Test Data, and Mathematical Observations, Color Research & Application 30(1), 21–30. The authors provide test data and discuss numerical pitfalls.

Color coordinates and reference light: CIE 015:2018, Colorimetry, fourth edition, covers standard observers, illuminants, XYZ, color spaces and color differences. The CIE also publishes its D50 spectral data.

These references explain the measurement language. The pattern comparisons, forecast outcomes, and chosen error limits on this page come from this project's experiments.

Exact row organization mattered even without changing orientation

These comparisons extend the same investigation beyond horizontal versus vertical. They keep the patterns horizontal and ask how the measured color changes when the row sequence, starting position, and run grouping change. Together, they show that orientation was only one way exact organization could change the measurement.

Same counts, different row order

This comparison kept both patterns horizontal and used the same 96,000 black, 192,000 yellow, and 96,000 blue pixels. One four-row period alternated yellow–blue–yellow–black; the other placed the two yellow rows together as yellow–yellow–blue–black. The display received two exact pixel arrangements, not two names for one image.

Cyclic: yellow · blue · yellow · black
Grouped: yellow · yellow · blue · black

Color change with the stripe axis fixed

The cyclic pattern measured lighter and more yellow in both presentation orders. Its signed Lab change was ΔL* +15.39 / +15.51 and Δb* +11.04 / +12.04.

Perceptual color distance

ΔE00 was 15.390 in the first order and 15.573 in the reversed order. This is an unsigned separation under nominal perfect-diffuser D50 convention. It describes color separation, not a visibility or significance verdict.

What the spectrum added

All 36 measured bands pointed in the same signed direction in both orders. Spectral RMS was 12.083 and 12.200 percentage points.

What repeating the order checked

The two signed spectral shapes had cosine 0.999900; their vector discrepancy was 0.207 percentage points RMS. A cosine close to 1 means the spectral changes point in nearly the same direction, even if their sizes differ. Vector discrepancy is the remaining difference between those two change spectra. Movement between repeat readings of the same pattern remains context, not an uncertainty limit.

Finding: the large measured contrast is not unique to turning horizontal stripes into vertical stripes. Overall color counts alone are insufficient to describe these two exact three-color pixel patterns. This does not prove that adjacency, grouping, or any other single construction detail caused the difference. These discovery comparisons did not test a model's absolute-color predictions. The later examples ask the broader question of predicting color on new inputs.

Compare starting position, grouping, and longer runs

Starting position, grouping, and matched summaries

Six four-reading comparisons separate three questions about organization. Every pattern kept the same black/yellow/blue counts and the same horizontal axis. A run is a band of consecutive rows with the same color. Boundary density describes how often neighboring rows change color. Each row remains its own descriptive result because it represents a different exact comparison; they are not averaged into one rule.

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Six completed comparisons, with color distance before spectral RMS
Arrangement questionOrderColor distance
ΔE00		Spectrum difference
pp RMS		Same-pattern movement
first / second, pp RMS
Move the starting row of the cyclic sequenceABBA0.3790.24250.1717 / 0.1051
Move the starting row of the cyclic sequenceBAAB0.2930.21100.0705 / 0.1298
Change cyclic rows into two-row runsRun length and boundary density change togetherABBA15.62612.20020.2227 / 0.0946
Change cyclic rows into two-row runsRun length and boundary density change togetherBAAB15.59612.16010.0851 / 0.0247
Compare two arrangements with the same simple summariesSame color counts, same number of boundaries, same counts of each run length, and same counts of which color directly followed whichABBA0.3850.36720.0992 / 0.0530
Compare two arrangements with the same simple summariesSame color counts, same number of boundaries, same counts of each run length, and same counts of which color directly followed whichBAAB0.4120.37220.0281 / 0.0657

Starting row

In this exact family, the 0.2425 / 0.2110 pp starting-phase differences were smaller than the large arrangement and run-grouping contrasts, but each was above both duplicate movements in its order (0.1717 / 0.1051 pp and 0.0705 / 0.1298 pp). Their signed directions also recurred across orders (cosine 0.9896). This does not predict what other starting positions would do or identify the physical cause.

Run grouping and boundaries

The large 12.2002 / 12.1601 pp difference recurred with nearly identical signed spectral direction (cosine 0.999986). Run length and boundary density changed together, so neither is isolated as the cause.

Matched simple summaries

The smaller 0.3672 / 0.3722 pp difference also recurred in direction (cosine 0.995871). Matching those summaries did not make the exact arrangements measure identically.

Combined finding: horizontal versus vertical was the opening clue, not the whole phenomenon. Exact fixed-axis arrangements can also measure differently. The experiment shows that keeping the horizontal direction fixed does not keep the measured color fixed. It does not yet tell us why, or how to predict another arrangement.

Longer row groups did not produce a proportional response

The comparison set repeats the cyclic-versus-two-row comparison, then compares two-row and four-row runs in both presentation orders. The exact black/yellow/blue counts and horizontal axis stayed fixed, while run length and boundary density still changed together.

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Three comparisons of row grouping, with color distance before spectral RMS
Arrangement questionOrderColor distance
ΔE00		Spectrum difference
pp RMS		Same-pattern movement
first / second, pp RMS
Compare cyclic rows with two-row runsRepeated alongside the longer-run comparisons in the same measurement sequenceABBA15.58812.16190.0827 / 0.0969
Compare two-row runs with four-row runsRun length and boundary density change togetherABBA2.2570.84910.0528 / 0.0555
Compare two-row runs with four-row runsRun length and boundary density change togetherBAAB2.2900.85910.0464 / 0.0390

The large contrast recurred

The 12.1619 pp cyclic-versus-two-row comparison pointed in almost the same signed spectral direction as the corresponding ABBA and BAAB rows (cosines 0.999992 and 0.999997).

The two-row-to-four-row contrast repeated

The two-row-to-four-row comparisons were 0.8491 and 0.8591 pp with cosine 0.99982394, magnitude ratio 1.01183170, and signed-vector discrepancy 0.01891485 pp RMS.

The change was not proportional

The two-row-to-four-row difference was about 7% of the cyclic-to-two-row difference's RMS and its spectral shape differed (cosine about 0.44). Run length and boundary density changed together; these observations do not define a proportional scaling law.

How this informed prediction: these comparisons motivated testing whether models could predict absolute color on new arrangements. The discovery rows still cannot establish a renderer rule or ICC correction by themselves.

Larger blocks did not always bring arrangements closer

A separate comparison used equal amounts of white, black, green and blue. It compared a regularly repeating arrangement with an irregular, computer-generated arrangement at two block sizes. With 2 × 2 same-color blocks, their measured colors were close; with 4 × 4 blocks, the difference was larger in both reading orders.

Color distance between the regular and irregular arrangements, ΔE00
Same-color blockABBABAAB
2 × 2 pixels0.2260.123
4 × 4 pixels2.2412.172

Enlarging the blocks also changed local color proportions and edge positions within the nominal measurement area; the meter’s exact spatial weighting was not established. This result argues against assuming that larger blocks always reduce arrangement-dependent differences, but it does not isolate block size as the cause.

What the prediction tests established →

Explore the individual measurements →