Accessibility: a validated colourblind-safe palette¶

depictr defaults to the Okabe-Ito palette and then measures what that choice buys. A Machado-2009 simulator and a CIE-Lab distance test confirm the colours stay distinguishable under each colour-vision deficiency. A safe palette is not a safe figure, though, so the same machinery also audits a finished plot. That is the second half of this page.

The safety report¶

The report gives the worst-case minimum distance between any two palette colours, across normal vision and each deficiency at full severity.

import depictr as dp

report = dp.palette_safety()
print(pre(repr(report)))

{'min_delta_e': 7.4, 'by_condition': {'normal': 33.43, 'protan': 18.15, 'deutan': 7.4, 'tritan': 16.18}, 'worst_condition': 'deutan', 'worst_pair': ('#cc79a7', '#999999'), 'safe': True, 'threshold': 5.0}

The palette in use¶

A grouped distribution in the default palette, a histogram with its density curve. legend_inside tucks the legend into the empty top-right corner, so the figure needs no separate margin.

ld = dp.lexical_decision()
p = dp.explore_distribution(ld, "RT", group="condition", kind="both",
                            legend_inside=True)
print(show(p))

The palette as a deficiency sees it¶

The same simulator drives the safety report above and the web app's colour-vision toggle. Below it maps every palette colour through each deficiency in turn, so the rows can be read against one another. The tightest pair is the reddish purple and the grey under deuteranopia, which is where the 7.4 in the report comes from, and even that stays well above the threshold of 5.

import pandas as pd
from plotnine import (aes, element_blank, geom_tile, ggplot, labs,
                      scale_fill_identity, scale_y_discrete, theme)

palette = dp.depictr_palette()
conditions = ["normal", *dp.cvd.DEFICIENCIES]

rows = []
for condition in conditions:
    # simulate_cvd takes the three deficiencies only; normal vision is the
    # palette itself, which is the same split palette_safety makes internally.
    seen = palette if condition == "normal" else dp.simulate_cvd(
        palette, condition
    )
    rows += [{"condition": condition, "position": i, "colour": colour}
             for i, colour in enumerate(seen)]

swatches = pd.DataFrame(rows)
p = (ggplot(swatches, aes("factor(position)", "condition", fill="colour"))
     + geom_tile(width=0.92, height=0.82)
     + scale_fill_identity()
     # Discrete scales are drawn from the bottom up, so the order is reversed
     # to put normal vision at the top.
     + scale_y_discrete(limits=list(reversed(conditions)))
     + labs(x="Palette colour", y=None)
     + theme(axis_text_x=element_blank(), panel_grid=element_blank()))
print(show(p, width=8, height=2.6))

The hex codes behind those rows, for the deficiency the palette comes closest to failing.

simulated = dp.simulate_cvd(palette, "deutan")
lines = [f"{original}  ->  {seen}"
         for original, seen in zip(palette, simulated)]
print(pre("\n".join(lines)))

#005b96  ->  #275295
#e69f00  ->  #cab411
#009e73  ->  #8a8676
#d55e00  ->  #9e8c00
#cc79a7  ->  #9498a5
#56b4e9  ->  #87a4e8
#f0e442  ->  #fce34e
#999999  ->  #999999

Where the guarantee stops¶

Eight colours is the guarantee, not a starting point. Asked for more, depictr_palette interpolates between the Okabe-Ito colours, and the in-between colours land close enough together that the same check fails them. The package warns when that happens, so no colours go out under a promise it cannot keep, and the honest reading of the report below is that nine groups is already the ceiling and ten is past it.

import warnings

with warnings.catch_warnings():
    warnings.simplefilter("ignore")  # the warning is the point; here we tabulate it
    sizes = {n: dp.palette_safety(dp.depictr_palette(n)) for n in (8, 9, 10, 12)}

lines = [f"n = {n:>2}   min Delta-E {r['min_delta_e']:>5}   safe: {r['safe']}"
         for n, r in sizes.items()]
print(pre("\n".join(lines)))

n =  8   min Delta-E   7.4   safe: True
n =  9   min Delta-E  5.63   safe: True
n = 10   min Delta-E  1.88   safe: False
n = 12   min Delta-E  3.92   safe: False

With more than eight groups, facet them, or map the variable to the sequential ramp (dp.depictr_palette(n, kind="sequential")), which stays ordered and legible at any length because lightness carries the ordering.

Auditing the figure you are about to submit¶

The palette report above describes eight colours in the abstract. It cannot know how many of them a given figure uses, what you replaced them with, how small the text becomes once the figure is squeezed into a journal column, or whether the only thing separating two groups is their colour. check_figure reads the built plot and reports what it measured beside the threshold it was measured against.

p = dp.explore_distribution(ld, "RT", group="condition", kind="both",
                            legend_inside=True)
print(table(dp.check_figure(p)))

check	measured	threshold	verdict	detail
colour_separability	119.21	5.0	pass	Closest pair #005b96 and #e69f00 of 2 encoding colours.
colour_separability_protan	108.92	5.0	pass	Closest pair #005b96 and #e69f00 of 2 encoding colours.
colour_separability_deutan	121.29	5.0	pass	Closest pair #005b96 and #e69f00 of 2 encoding colours.
colour_separability_tritan	77.90	5.0	pass	Closest pair #005b96 and #e69f00 of 2 encoding colours.
greyscale_separability	33.34	5.0	pass	Closest pair #005b96 and #e69f00 in CIE lightness.
text_size	8.80	6.0	pass	Smallest text 8.80 pt, drawn at 17.78 cm and printed at 17.78 cm.
text_contrast	8.45	4.5	pass	Lowest-contrast text #4d4d4d on #ffffff.
geometry_contrast	2.25	3.0	fail	Lowest-contrast colour #e69f00 on #ffffff.
redundant_encoding	0.00	1.0	fail	Colour alone distinguishes the groups.

Two rows are worth dwelling on. geometry_contrast measures each encoding colour against the panel background, and the palette's orange sits at 2.25 against white, below the 3:1 that WCAG asks of a graphical object. redundant_encoding is zero because nothing but colour tells the two conditions apart. The audit also takes a stated output width, which is where most figure text quietly fails: text is drawn in points, so a figure saved seven inches wide and then printed in an 8.9 cm column arrives at half the size it looked on screen.

column = dp.check_figure(p, width_cm=8.9)
print(table(column[column["check"] == "text_size"]))

check	measured	threshold	verdict	detail
text_size	4.4	6.0	fail	Smallest text 8.80 pt, drawn at 17.78 cm and printed at 8.90 cm.

A figure built with two well-separated colours, a redundant shape and no shrinking clears every row, so the audit returns a pass as readily as a failure.

from plotnine import aes, geom_point, ggplot, scale_colour_manual

cy = dp.crop_yield()
mended = (ggplot(cy, aes("rainfall", "yield", colour="treatment",
                         shape="treatment"))
          + geom_point(alpha=0.7)
          + scale_colour_manual(values=["#005b96", "#d55e00"])
          + dp.theme_depictr())
print(table(dp.check_figure(mended)[["check", "measured", "threshold",
                                     "verdict"]]))

check	measured	threshold	verdict
colour_separability	111.87	5.0	pass
colour_separability_protan	89.87	5.0	pass
colour_separability_deutan	107.07	5.0	pass
colour_separability_tritan	98.50	5.0	pass
greyscale_separability	16.92	5.0	pass
text_size	8.80	6.0	pass
text_contrast	8.45	4.5	pass
geometry_contrast	3.87	3.0	pass
redundant_encoding	1.00	1.0	pass

Where the guarantee stops a second time: greyscale¶

One limitation belongs here, where the claim is made. The eight-colour palette clears every colour-vision check and fails the greyscale check: its orange and its sky blue differ by 0.79 in CIE lightness, so a black-and-white printer renders them as the same grey. The Okabe-Ito guarantee is about hue confusion and was never a claim about greyscale. Moving the threshold would let depictr's own defaults through, so it stays where it is.

eight = pd.DataFrame({"g": list("abcdefgh"), "x": range(8), "y": range(8)})
p8 = (ggplot(eight, aes("x", "y", colour="g")) + geom_point()
      + dp.scale_colour_depictr() + dp.theme_depictr())
report = dp.check_figure(p8)
print(table(report[report["check"].str.contains("separability")]))

check	measured	threshold	verdict	detail
colour_separability	33.43	5.0	pass	Closest pair #d55e00 and #e69f00 of 8 encoding colours.
colour_separability_protan	18.15	5.0	pass	Closest pair #999999 and #cc79a7 of 8 encoding colours.
colour_separability_deutan	7.40	5.0	pass	Closest pair #999999 and #cc79a7 of 8 encoding colours.
colour_separability_tritan	16.18	5.0	pass	Closest pair #009e73 and #56b4e9 of 8 encoding colours.
greyscale_separability	0.79	5.0	fail	Closest pair #56b4e9 and #e69f00 in CIE lightness.

A figure that may be printed in black and white wants fewer groups, a sequential palette, or a redundant shape or line type. Four groups are not enough on their own either: the bluish green and the vermillion differ by 3.55.