Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
And whatever I do will become forever what I've done.Wislawa Szymborskadon't rehearsemore quotes


In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017


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.

Visions of Type

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

Below I show the difference between Andrew's version of Snellen and my own redesign of the font—read about redesign process—which reinterprets some of the characters and adds lowercase.

You can download both versions of the font.

Characters in the Snellen TrueType font and my redesign of some of the characters. / 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

Statistics vs Machine Learning

Tue 03-04-2018
We conclude our series on Machine Learning with a comparison of two approaches: classical statistical inference and machine learning. The boundary between them is subject to debate, but important generalizations can be made.

Inference creates a mathematical model of the datageneration process to formalize understanding or test a hypothesis about how the system behaves. Prediction aims at forecasting unobserved outcomes or future behavior. Typically we want to do both and know how biological processes work and what will happen next. Inference and ML are complementary in pointing us to biologically meaningful conclusions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Statistics vs machine learning. (read)

Statistics asks us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities. Justification for an inference model typically rests on whether we feel it adequately captures the essence of the system. The choice of pattern-learning algorithms often depends on measures of past performance in similar scenarios.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Statistics vs machine learning. Nature Methods 15:233–234.

Background reading

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: supervised methods. Nature Methods 15:5–6.

...more about the Points of Significance column

Happy 2018 `\pi` Day—Boonies, burbs and boutiques of `\pi`

Wed 14-03-2018

Celebrate `\pi` Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.

Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)

Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In the Boonies, Burbs and Boutiques of `\pi` we draw progressively denser patches using the digit sequence 159 to inform density. (details)

No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Roads from cities rearranged according to the digits of `\pi`. (details)

The art is featured in the Pi City on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day and 2017 `\pi` Day.

Machine learning: supervised methods (SVM & kNN)

Thu 18-01-2018
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Background reading

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

...more about the Points of Significance column

Human Versus Machine

Tue 16-01-2018
Balancing subjective design with objective optimization.

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

Machine learning: a primer

Thu 18-01-2018
Machine learning extracts patterns from data without explicit instructions.

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Machine learning: a primer. (read)

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

...more about the Points of Significance column