Poetry is just the evidence of life. If your life is burning well, poetry is just the ashburn somethingmore quotes

# typography: beautiful

DNA on 10th — street art, wayfinding and font

# 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

SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. (zoom)
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 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.

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.
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.
$E FP NBJ GCHQ RKVNX PZLSAY IMEXDBU CYRAVQGH LWKPIJZO XUBHRFEV JTDIGSYZ QFWLMUKA$
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
$A TG CAT ATCG GCATA CGTCTG TACAGAC GTGTACGA CGAGCTAT ACTCTGTG GTCAGAGC CGAGATAG$
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!

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

Snellen Chart of abundance of the elements in the universe. (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.

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 $\triangleleft$.

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.

Snellen Chart typeset in Braille. (BUY ARTWORK)
Snellen Chart typeset in Braille. Variant #2. (BUY ARTWORK)
Snellen Chart typeset in Braille. Variant #3. (BUY ARTWORK)
VIEW ALL

# Yearning for the Infinite — Aleph 2

Mon 18-11-2019

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.

# Hidden Markov Models

Mon 18-11-2019

Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

Nature Methods Points of Significance column: Hidden Markov Models. (read)

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (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.

# Hola Mundo Cover

Sat 21-09-2019

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

Hola Mundo by Hannah Fry. Cover design is based on my 2013 $\pi$ day art. (read)

Curious how the design was created? Read the full details.

# Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

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

# 1-bit zoomable gigapixel maps of Moon, Solar System and Sky

Mon 22-07-2019

Places to go and nobody to see.

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)
100 megapixel and 10 gigapixel map of the Solar System on 20 July 2019, annotated with 758k asteroids, 1.3k comets and all planets and satellites. (details)
100 megapixle and 10 gigapixel map of the Northern Celestial Hemisphere, annotated with 44 million stars, 74,000 deep-sky objects and 3,000 exoplanets. (details)
100 megapixle and 10 gigapixel map of the Southern Celestial Hemisphere, annotated with 69 million stars, 88,000 deep-sky objects and 1000 exoplanets. (details)