Saturday, 16 October 2021


I've just been baking. But what do you think of when you see the results?

  1. Biscuits
  2. Cookies
  3. Voronoi

Depending on your answer:

  1. You're probably British
  2. You're probably American
  3. You're definitely a geek

Thursday, 7 October 2021

Machin Postage Stamps 3

I've done some investigation into Machin stamp designs that take into account colour vision deficiency (CVD). In particular, I looked at CVD-safe colour schemes and visual representation of numerals for the denominations. See those three web pages for more details.

The numeral scheme I finally came up with (after a lot of experimentation) is as follows:

The symbols have the following properties:

  1. The number of small dots is the value of the digit.
  2. Each has a high-contrast, CVD-safe colour (from the 'Chilliant Pale/Deep 19' palette).
  3. The outlines are distinct.
  4. They all fit within a circle the size of the grey ring zero.

For dark backgrounds, simply switch the pale/deep pairings:

The names I've ascribed to each of the symbols are:

  • 0: grey ring
  • 1: slate circle
  • 2: brown oval
  • 3: purple triangle
  • 4: cyan cross
  • 5: green bowtie
  • 6: pink star
  • 7: blue heptagon
  • 8: orange square
  • 9: mint lozenge

Monday, 4 October 2021


Machin stamps are colour-coded according to their denomination. The coding scheme is somewhat ad hoc. But what if we wanted to be more systematic?

There are surprising few existing systems for encoding numbers as colours. One is the old system used for electronic components:

The digits zero to nine are represented by ten colours. My favourite mnemonic is:

Black Bananas Really Offend Your Girlfriend, But Violets Get Welcomed

In the past, colour-blind people were allegedly discouraged from becoming electricians because of the possibility of confusing earth (green), live (red) and neutral (black) in the pre-1977 UK domestic mains cabling colour scheme.

In an ideal world, the mapping of colours to numeric values would be fairly immune to any colour vision deficiency (CVD) experienced by the viewer. This led me to an investigation into colour-blindness: what used to be called "Daltonism" in the UK.

There are plenty of resources on the web explaining the various forms of colour blindness, but I wanted to be able to objectively assess how "good" a palette of colours was for:

  1. People with no colour deficiency (I'll call them "trichromats"),
  2. People with protanopia, deuteranopia or tritanopia ("dichromats"), and
  3. People with monochrome vision ("monochromats").

One metric of how well a palette of colours "fills" a colour space is to measure the minimum "distance" between any two entries. I chose the CIELAB colour space and the CIEDE2000 metric because they were close-at-hand as part of my previous Goldenrod project.

I defined lambda as the minimum distance (ΔE2000) between colours in the palette as seen by trichromats; also known as minD(normal). The greater this number, the less likely that two entries within the palette will be confused by trichromats.

I then used a corrected version of Color.Vision.Simulate from HCIRN to simulate the four colour deficiencies and produce four "confused" palettes from the original:

  1. protanope
  2. deuteranope
  3. tritanope
  4. achromatope

Each of the confused palettes will have a minimum distance between colours within them; call these minimum distances minD(protanope), etc.

I defined beta as the minimum of minD(protanope), minD(deuteranope) and minD(tritanope). The greater this number, the less likely that two entries within the original palette will be confused by dichromats. I appreciate that there are far fewer sufferers of tritanopia in the general population than of the other two forms of dichromatism, but I haven't scaled the three distance metrics accordingly; I'm running under the premise of "none left behind".

I defined alpha to be minD(achromatope). The greater this number, the less likely that two entries within the original palette will be confused by monochromats.

Finally, I defined omega to be the minimum distance between two adjacent CIELChab hues from the original palette, measured in degrees. This number measures hue separation perceived by trichromats.

In summary:

  • Lambda, λ, is "min ΔE2000" for the original, trichromatic palette. It measures how different the colours in the palette seem to a viewer with no colour vision deficiency. Larger values indicate greater variation.
  • Beta, β, is the least "min ΔE2000" for the dichromatic remappings of the palette. It measures how different the colours in the palette seem to a viewer with one of those colour vision deficiencies. Larger values indicate greater variation.
  • Alpha, α, is "min ΔE2000" for the achromatic remapping of the palette. It measures how different the colours in the palette seem to a viewer with achromatopsia, when rendered in greyscale or in some low-light conditions. Larger values indicate greater variation.
  • Omega, ω, is "min Δhab" for the original, trichromatic palette. It measures the perceived hue separation (measured in degrees) experienced by a viewer with no colour vision deficiency. Larger values indicate greater separation.

Unfortunately, as the number of entries in a palette increases, we expect the λ, β, α and ω scores to decrease, so we cannot easily compare palettes with differing numbers of entries. Perhaps the scores could be scaled depending on the palette size, but I haven't tried to work out the factor; I suspect it's not linear.

In general, for our purposes, a "good" palette is one with high λ, β and/or α scores. Maximising λ is appropriate for about 92% of the population; β for about 8%; and α for less than 0.01%.

The accompanying web page computes the scores for existing and novel palettes.

If we take "Chilliant Pale/Deep 19" from that page and re-order the palette into hue order, we get a colour-blind-friendly scheme with which to encode the digits zero to nine:

This could be the basis for a new colour-coding of stamp denominations...

Friday, 17 September 2021

Unicode Numeral Systems

As part of my investigations into Machin stamps, I started looking at numeral systems for labelling stamp denominations and also clock faces.

Unicode 13.0.0 contains a few General Categories used to classify code points according to numeric value ("Nd", "Nl" & "No") plus Derived Numeric Types ("Decimal", "Digit" & "Numeric"). Trawling through these and the Wikipedia pages on numeral systems, I came up with well over one hundred systems that can be used to represent numbers in Unicode using single glyphs:

Unicode Numerals web page

As it turns out, this experiment became more of an exercise in font management. I initially used Unifont for rendering, but this is quite ugly. The Code2000 fonts are no longer maintained. I ended up using Googles Noto fonts. However, there doesn't seem to be a definitive list of which glyphs exist in which font, so I had to create a tool to interrogate all the Noto web fonts I could find. Even an online list of those web fonts seems lacking, so here's one:

  • Noto Kufi Arabic
  • Noto Naskh Arabic
  • Noto Naskh Arabic UI
  • Noto Nastaliq Urdu
  • Noto Sans
  • Noto Sans JP
  • Noto Sans KR
  • Noto Sans SC
  • Noto Sans TC
  • Noto Sans Adlam
  • Noto Sans Adlam Unjoined
  • Noto Sans Anatolian Hieroglyphs
  • Noto Sans Arabic
  • Noto Sans Arabic UI
  • Noto Sans Armenian
  • Noto Sans Avestan
  • Noto Sans Balinese
  • Noto Sans Bamum
  • Noto Sans Batak
  • Noto Sans Bengali
  • Noto Sans Bengali UI
  • Noto Sans Bhaiksuki
  • Noto Sans Brahmi
  • Noto Sans Buginese
  • Noto Sans Buhid
  • Noto Sans Canadian Aboriginal
  • Noto Sans Carian
  • Noto Sans Chakma
  • Noto Sans Cham
  • Noto Sans Cherokee
  • Noto Sans Coptic
  • Noto Sans Cuneiform
  • Noto Sans Cypriot
  • Noto Sans Deseret
  • Noto Sans Devanagari
  • Noto Sans Devanagari UI
  • Noto Sans Display
  • Noto Sans Egyptian Hieroglyphs
  • Noto Sans Ethiopic
  • Noto Sans Georgian
  • Noto Sans Glagolitic
  • Noto Sans Gothic
  • Noto Sans Gujarati
  • Noto Sans Gujarati UI
  • Noto Sans Gurmukhi
  • Noto Sans Gurmukhi UI
  • Noto Sans Gunjala Gondi
  • Noto Sans Hanifi Rohingya
  • Noto Sans Hanunoo
  • Noto Sans Hebrew
  • Noto Sans Imperial Aramaic
  • Noto Sans Indic Siyaq Numbers
  • Noto Sans Inscriptional Pahlavi
  • Noto Sans Inscriptional Parthian
  • Noto Sans Javanese
  • Noto Sans Kaithi
  • Noto Sans Kannada
  • Noto Sans Kannada UI
  • Noto Sans Kayah Li
  • Noto Sans Kharoshthi
  • Noto Sans Khmer
  • Noto Sans Khmer UI
  • Noto Sans Khudawadi
  • Noto Sans Lao
  • Noto Sans Lao UI
  • Noto Sans Lepcha
  • Noto Sans Limbu
  • Noto Sans Linear B
  • Noto Sans Lisu
  • Noto Sans Lycian
  • Noto Sans Lydian
  • Noto Sans Malayalam
  • Noto Sans Malayalam UI
  • Noto Sans Mandaic
  • Noto Sans Masaram Gondi
  • Noto Sans Mayan Numerals
  • Noto Sans Medefaidrin
  • Noto Sans MeeteiMayek
  • Noto Sans Mende Kikakui
  • Noto Sans Meroitic
  • Noto Sans Modi
  • Noto Sans Mongolian
  • Noto Sans Mono
  • Noto Sans Mro
  • Noto Sans Myanmar
  • Noto Sans Myanmar UI
  • Noto Sans New Tai Lue
  • Noto Sans Newa
  • Noto Sans Ogham
  • Noto Sans Ol Chiki
  • Noto Sans Old Italic
  • Noto Sans Old Persian
  • Noto Sans Old South Arabian
  • Noto Sans Old Turkic
  • Noto Sans Oriya
  • Noto Sans Oriya UI
  • Noto Sans Osage
  • Noto Sans Osmanya
  • Noto Sans Pahawh Hmong
  • Noto Sans Phags Pa
  • Noto Sans Phoenician
  • Noto Sans Rejang
  • Noto Sans Runic
  • Noto Sans Samaritan
  • Noto Sans Saurashtra
  • Noto Sans Sharada
  • Noto Sans Shavian
  • Noto Sans Sinhala
  • Noto Sans Sinhala UI
  • Noto Sans Sundanese
  • Noto Sans Syloti Nagri
  • Noto Sans Symbols
  • Noto Sans Symbols 2
  • Noto Sans Syriac
  • Noto Sans Tagalog
  • Noto Sans Tagbanwa
  • Noto Sans Tai Le
  • Noto Sans Tai Tham
  • Noto Sans Tai Viet
  • Noto Sans Takri
  • Noto Sans Tamil
  • Noto Sans Tamil UI
  • Noto Sans Telugu
  • Noto Sans Telugu UI
  • Noto Sans Thaana
  • Noto Sans Thai
  • Noto Sans Thai UI
  • Noto Sans Tifinagh
  • Noto Sans Tirhuta
  • Noto Sans Ugaritic
  • Noto Sans Vai
  • Noto Sans Wancho
  • Noto Sans Warang Citi
  • Noto Sans Yi
  • Noto Serif
  • Noto Serif JP
  • Noto Serif KR
  • Noto Serif SC
  • Noto Serif TC
  • Noto Serif Ahom
  • Noto Serif Armenian
  • Noto Serif Bengali
  • Noto Serif Devanagari
  • Noto Serif Display
  • Noto Serif Ethiopic
  • Noto Serif Georgian
  • Noto Serif Gujarati
  • Noto Serif Hebrew
  • Noto Serif Kannada
  • Noto Serif Khmer
  • Noto Serif Lao
  • Noto Serif Malayalam
  • Noto Serif Myanmar
  • Noto Serif Nyiakeng Puachue Hmong
  • Noto Serif Sinhala
  • Noto Serif Tamil
  • Noto Serif Telugu
  • Noto Serif Thai
  • Noto Serif Tibetan

The Font Check tool allows you to type in a hexadecimal Unicode code point and see the fonts that can render it. It uses the trick of measuring the glyph using an offscreen canvas with a fallback font of Adobe Blank. If the glyph is zero pixels wide, it means it was rendered using the fallback (or is naturally zero-width, so isn't of interest to us anyway).

Using the tool, I worked out the minimal set of Noto fonts needed to render the numerals table. However, there were a few issues:

  1. Some fonts only come in serif variants, not sans serif (and vice versa).

  2. I couldn't find any Noto web fonts that could render the following (though the asterisked scripts were rendered correctly using a fallback font by my browser):

    • Dives Akuru
    • Khmer Divination*
    • Myanmar Tai Laing*
    • Nko*
    • Ottoman Siyaq
    • Sinhala*
    • Sora Sompeng*
    • Tag

  3. Arabic Persian and Arabic Urdu use exactly the same codepoints but use different languages in the HTML mark-up to select different sets of glyphs.

Further notes:

  • I couldn't find any information on how Ogham represented numbers, so I made something up based on tally marks.
  • The Tibetan script has a parallel set of numerals for half values; they're used in stamps, which is a nice coincidence.
  • The Runic Golden Numbers are used in Younger Futhark calendars.
  • Other scripts do have numerals or counting systems, but I excluded many because they are "low radix" (e.g. native Korean)

Monday, 13 September 2021

Machin Postage Stamps 2

Well, I thought I was being clever, didn't I? Using WebP images for Machin stamps. Alas, WebP has only recently been supported by Apple's Safari, so the web page didn't work at all on an older model iPad.

My original HTML was simply:

<img id="picture" class="shadow" src="machin.webp" />

And the source image path was accessed from JavaScript via:


The fix from Brett DeWoody is actually quite elegant. Change the HTML to use picture source sets:

<picture class="shadow">
    <source srcset="machin.webp" type="image/webp" />
    <img id="picture" src="machin.png" />

And use the following to interrogate the chosen path after load:


Wednesday, 25 August 2021

Machin Postage Stamps 1

There is a web page to accompany these blog posts.

I was sorting through some old family papers when I came across my father's stamp collection. He had a number of unsorted UK stamps that I (being me) decided to organise.

Arnold Machin

The Machin series of UK postage stamps are named after the sculptor (Arnold Machin, 1911-1999) who designed them. His profile of Queen Elizabeth II has been used on many coins and stamps:

Pre-Decimal Machin Stamps

The original, pre-decimal stamps to use the Machin profile (from 1967 onwards) came in denominations of:

½d, 1d, 2d, 3d, 4d, 5d, 6d, 7d, 8d, 9d, 10d, 1/-, …

Each denomination had a different colour, although I'm fairly certain there was no systematic colour scheme.

I found all of the denominations, up to and including the shilling, in my father's collection, so I thought about how to mount them in a display. These stamps aren't very valuable, so permanently sticking them to a bit of card isn't so terrible.

My first thought was just a grid:

Or perhaps a circular layout:

At this point, I was reminded of a clock face. Alas, there was never a "11d" Machin stamp, but one could swap the half penny and shilling stamps and use "½d" for eleven o'clock and "1/-" for twelve o'clock:

Here's a mock-up of a clock built around this layout:

I also built a JavaScript demo loosely based on a beautiful CSS-only clock by Nils Rasmusson.

Decimal Machin Stamps

Next I moved on to the Machin stamps used after decimalisation in 1971. These had all the half-penny increments up to and including 13½p, so two rings could be constructed:

Or, with axis-aligned stamps:

These templates are available on the web page as SVGs with absolute measurements: each stamp is 21mm by 24mm. You can print out the desired page at 100% scale and use the templates when mounting the stamps. Unfortunately the "double ring" layouts don't quite fit on a single sheet of A4 so you'll need to crop and rely on symmetry to physically flip the template.


I decided to mount 23 stamps (my father never acquired a "11½p" Machin) using the last template within a 240mm-by-300mm frame:

  1. Print out the template at 100% scale.
  2. Carefully cut along three sides of each stamp "window" with a scalpel.
  3. Position the template over the mounting card.
  4. Secure the template to the mounting card with masking tape. Try to avoid sticking the tape directly to the front of the card. (Figure 1)
  5. Stick the appropriate stamps on to the card using double-sided tape through the windows. (Figure 2)
  6. Carefully remove the template and insert the mounting card into the frame. (Figure 3)
Figure 1

Figure 2

Figure 3

There's a conspicuous gap where the missing stamp should go. I could fill it by splurging a couple of quid on ebay, but the gap itself has a story.

Another project would be to affix a cheap battery quartz movement to a similar clock face. I had hoped to use an old CD for the circular face, but I don't think twelve stamps quite fit.

Tuesday, 24 August 2021

Gratuitous Aphorism #8

Experts are just people who have already made all the silly mistakes.