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See you at Shonan Meeting 167 — Formalizing Biomedical Visualization


art + design

Math geek? If you like the clean geometric design of the type posters, you may enjoy something even more mathematical. Design that transcends repetition: Art of Pi, Phi and e posters.
Are optotypes your type?
SnellenMK adds lowercase and punctuation to the traditional Snellen design.

Visions of Type

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. (zoom)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. (zoom)

eyes on the universe

These typographical posters are designed after the style of the Snellen Chart, which is one of the kinds of eye charts used to measure visual acuity.

If you love looking, seeing and the universe, these posters are for you. They are available for purchase.

optotypes

Symbols on such charts are known as optotypes. Fonts by Andrew Howlett exist whose glyphs conform to the properties of optotypes: Snellen font and Sloan font. However, some of the characters in the Snellen font file are a little oddly shaped—I provide my redesign of the Snellen font in which the glyphs are more consistent (see below). Lowercase characters are not available.

For the posters here, I've used either my redesigned Snellen font or Monotype's Rockwell, with minor stroke and kerning adjustments in places. Some symbols, such as on the math chart, were designed by hand.

The numbers on the left side of the posters (e.g. 20/30) are a measure of visual acuity. The numbers on the right provide information about what is shown on the line (e.g. abundance of elements).

Snellen chart design

The charts are designed to be viewed at a distance of 6 meters (20 feet). At this distance, ability to resolve a letter tha subtends 5 minute of arc corersponds to 6/6 (or 20/20) visual acuity. This corresponds to a letter size of $$\frac{2\pi}{360} \times \frac{5}{60} \times 6 = 8.727 \, \text{mm} = 24.74 \, \text{pt}$$

The Snellen optotypes are designed on a 5 × 5 grid and have a fascinating history. For design, Rockwell and Lubalin Graph can be used to approximate Snellen, though these fonts lack the grid structure of the optotypes.

Snellen optotypes of the 9 letters used in eye charts. The optotypes are compared to characters from the Rockwell Bold font. / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Snellen optotypes are designed on a 5 × 5 grid. At a viewing distance of 6 m (20 ft) each letter on the 6/6 (or 20/20) acuity line must be 8.727 mm (24.47 pt). The optotypes are compared to the characters from the Rockwell Bold font, which is a mediocre approximation. (zoom)

snellen optotype font

My redesign of Andrew Howlett's Snellen optotype font. Read about redesign process—which reinterprets some of the characters and adds lowercase.

You can download both versions of the font.

Glyph chart of my Snellen optotype font. / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Snellen optotypes are designed on a 5 × 5 grid. At a viewing distance of 6 m (20 ft) each letter on the 6/6 (or 20/20) acuity line must be 8.727 mm (24.47 pt) (zoom, zoom, about the design, download Snellen font)

the posters

conventional Snellen charts

These Snellen charts include acuity lines from 20/200 to 20/10.

The charts should be printed at a physical size of 16" × 24" (1150 pt × 1725 pt. At this size, the characters on the 20/20 line subtend 5 minutes of arc when viewed at 6 meters (20 feet), which is the technical specification of the Snellen chart.

When the charts are printed at this size, the two horizontal lines below the 20/30 and 20/20 lines are exactly 8" (576 pt) long. These length markers are my own addition.

If the chart is printed at any other size, the viewing distance changes. To compute the correct viewing distance, `d`, measure the length of these lines, `L` (in inches) and use $$ d = 6 \times L / 8 $$

For example, if I print this chart to fit onto an 8.5" × 11" page, these lines are 3.47". Thus, my smaller chart should be viewed from `6 \times 3.47 / 8 = 2.60 \, \text{m}` (8.53 ft).

Numbers on the left provide visual acuity in feet. Numbers on the right show the denominator of the acuity in feet and its equivalent in meters, rounded to the nearest integer.

The order of the 61 characters on the charts has been limit uniformity and avoid easily perceived patterns—especially in the case of the genetic sequence Snellen. These restrictions (e.g. limit in the number of repeated n-grams) apply across linebreaks.

9 character Snellen

This is the canonical Snellen chart, using the 9 original characters.

E FP LDO CETD ZOFEL DCZTFP PFLOZDE OZPCELTD TLEFDCOP EDOPTFLC LTCZOEPF FODLPZCT
  1. no more than 8 instances of any character and no fewer than 6
  2. no double characters (e.g. PP does not occur)
  3. no more than 2 repeats of any 2-gram (e.g. LT ... LT ... LT does not occur)
  4. all 3-grams are unique (e.g. LDO does not repeat)
  5. no identical adjacent characters across lines within a distance of one positions.
  6. for a given line, the characters at the same position in the previous 6 lines are all different.

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
A technically accurate Snellen chart using traditional 9 characters C D E F L O P T Z rendered as optotypes. Print at 16 in × 24 in. (BUY ARTWORK)

26 character Snellen

This chart uses all the letters of the alphabet and is typset using my Snellen font redesign.

  1. all letters of the alphabet are used
  2. no more than 3 instances of any character
  3. no double characters (e.g. PP does not occur)
  4. all n-grams (n = 2, 3, ...) are unique
  5. on a given line, all characters are unique
  6. no identical adjacent characters across lines within a distance of 8 positions.
  7. for a given line, the characters at the same position in all other lines are all different.
E FP NBJ GCHQ RKVNX PZLSAY IMEXDBU CYRAVQGH LWKPIJZO XUBHRFEV JTDIGSYZ QFWLMUKA

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
A technically accurate Snellen chart using all 26 letters of the alphabet rendered as optotypes. All n-grams are unique. Print at 16 in × 24 in. (BUY ARTWORK)

genomic sequence Snellen

Since I work in a genome center, the one below is the one we'd use. Thanks to Dr. Nüket Bilgen for suggesting that the chart start with ATG (start codon) and end with one of the stop codons (TAG, TGA, but not TAA since no two adjoining characters can be the same).

  1. no more than 19 instances of any character and no fewer than 15
  2. no double characters (e.g. AA does not occur)
  3. no more than 7 repeats of any 2-gram
  4. no more than 4 repeats of any 3-gram
  5. no more than 2 repeats of any 4-gram or 5-gram
  6. for a given line, the characters at the same position in the previous 2 lines are different
  7. chart starts with start codon ATG
  8. chart ends with stop codon TAG, which appears only once; the other two stop codons (TGA, TAA) do not appear on the chart
A TG CAT ATCG GCATA CGTCTG TACAGAC GTGTACGA CGAGCTAT ACTCTGTG GTCAGAGC CGAGATAG

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
A technically accurate Snellen chart using four genetic bases A T G C rendered as optotypes. The chart begins with the start codon ATG and ends in the stop codon TGA, which appears only once in the chart. Print at 16 in × 24 in. (BUY ARTWORK)

The best alignments of this chart's sequence are to fungus (Leptosphaeria maculans lepidii, 35/42, 83%) and a tapeworm (Diphyllobothrium latum, 24/26, 92%). Thanks to Lorraine May for this observation!

nautical flags Snellen

Charts ahoy!

Z KE CHG XVRM YTWUS JQFINB EZAOXLD NHKVCUGF SWRMIAZP DBTOJYXE FZHLNUKA IVGMYCWR

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
A technically accurate Snellen chart using the nautical flag alphabet rendered as optotypes. Print at 16 in × 24 in. (BUY ARTWORK)

The flag alphabet has been designed to match, as closely as possible, to the style of the Snellen optotypes. In some cases this required that the geometry of the flag had to be adjusted—this may upset the purists and cause havoc on the waterways.

Proportions of colors has been adjusted in some flags to fit symmetrically into the 5 × 5 optotype grid. The checker of N is now a 5 × 5 grid. The number of stripes in Y has been reduced—the width of each stripe is now 20% of the width of the flag. Proportions in C, D, J, R, S, T, W and X have been adjusted so that color strips are a multiple of 20% of the width of the flag. The cross in M and V matches the X used in the Snellen font.

Snellen optotypes for the nautical flag alphabet. / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Snellen optotypes for the nautical flag alphabet. (zoom)

eyes on the elements

Elements are sorted in order of abundance. The numbers on the left show the max and min `-log_{10}` abundance of the elements listed on a given line. For example, 3.0/3.3 for the "N Si Mg S" line in the abundance of elements in the universe indicates that abundance of N is 0.001 and of S is 0.0005.

You can download my tidy plain-text table of abundance of elements in the universe (original source, 83 elements) and table of abundance of elements in the body (original source, 60 elements). These have been parsed from the original sources and give the `-log_{10}` abundance for various elements.


Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart of abundance of the elements in the universe. (BUY ARTWORK)

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart of abundance of the elements in the human body. (BUY ARTWORK)

eyes on physical constants

44 of the most interesting physical constants ranging from the very large (Planck temperature `T_p = 1.4 \times 10^{32} \mathrm{K}`) to the very small (cosmological constant `\Lambda = 1.19 \times 10^{-52} \mathrm{m}^{-2}`). You can download the table of constants and their values.


Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart of physical constants. (BUY ARTWORK)

eyes on mathematical symbols

44 intriguing and perhaps mysterious mathematical symbols ranging from common equality `=` to the esoteric normal subgroup `\triangleleft`.


Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart of mathematical operators and symbols. (BUY ARTWORK)

where's the chart?

The chart is the visual form of a rhetorical question. The letter layout here is the same as in the canonical Snellen chart, which is limited to the 10 Sloan letters C, D, E, F, L, N, O, P, T, Z.


Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart typeset in Braille. (BUY ARTWORK)

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart typeset in Braille. Variant #2. (BUY ARTWORK)

Typographical posters of how the world works in the style of Snellen eye charts
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Snellen Chart typeset in Braille. Variant #3. (BUY ARTWORK)
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news + thoughts

Using Circos in Galaxy Australia Workshop

Thu 20-02-2020

A workshop in using the Circos Galaxy wrapper by Rasche and Hiltemann. Event organized by Australian Biocommons.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Using Circos in Galaxy Australia workshop. (zoom)

Download workshop slides.

Galaxy wrapper training materials, Saskia Hiltemann, Helena Rasche, 2020 Visualisation with Circos (Galaxy Training Materials).

Essence of Data Visualization in Bioinformatics Webinar

Thu 20-02-2020

My webinar on fundamental concepts in data visualization and visual communication of scientific data and concepts. Event organized by Australian Biocommons.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Essence of Data Visualization in Bioinformatics webinar. (zoom)

Download webinar slides.

Markov models — training and evaluation of hidden Markov models

Thu 20-02-2020

With one eye you are looking at the outside world, while with the other you are looking within yourself.
—Amedeo Modigliani

Following up with our Markov Chain column and Hidden Markov model column, this month we look at how Markov models are trained using the example of biased coin.

We introduce the concepts of forward and backward probabilities and explicitly show how they are calculated in the training process using the Baum-Welch algorithm. We also discuss the value of ensemble models and the use of pseudocounts for cases where rare observations are expected but not necessarily seen.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Markov models — training and evaluation of hidden Markov models. (read)

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov models — training and evaluation of hidden Markov models. Nature Methods 17:121–122.

Background reading

Altman, N. & Krzywinski, M. (2019) Points of significance: Hidden Markov models. Nature Methods 16:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

Genome Sciences Center 20th Anniversary Clothing, Music, Drinks and Art

Tue 28-01-2020

Science. Timeliness. Respect.

Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Luke and Mayia wearing limited edition volunteer t-shirts. The pattern reproduces the human genome with chromosomes as spirals. (zoom)

As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Precisely engineered frame mounts of flow cells used to sequence genomes in our laboratory. (zoom)

Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The plaque at the back of one of the framed Illumina flow cell. This one has sequence from a patient's lymph node diagnosed with Burkitt's lymphoma. (zoom)

Scientific data visualization: Aesthetic for diagrammatic clarity

Mon 13-01-2020

The scientific process works because all its output is empirically constrained.

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.