Visions of Type
contents
- 1 · A font to test your eyes
- 2 · Optotypes
- 3 · Snellen chart design
- 4 · Snellen optotype font
- 5 · Classic and modern eyechart posters
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.
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).
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.
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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.
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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.
This is the canonical Snellen chart, using the 9 original characters.
E FP LDO CETD ZOFEL DCZTFP PFLOZDE OZPCELTD TLEFDCOP EDOPTFLC LTCZOEPF FODLPZCT
- no more than 8 instances of any character and no fewer than 6
- no double characters (e.g. PP does not occur)
- no more than 2 repeats of any 2-gram (e.g. LT ... LT ... LT does not occur)
- all 3-grams are unique (e.g. LDO does not repeat)
- no identical adjacent characters across lines within a distance of one positions.
- for a given line, the characters at the same position in the previous 6 lines are all different.
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This chart uses all the letters of the alphabet and is typset using my Snellen font redesign.
- all letters of the alphabet are used
- no more than 3 instances of any character
- no double characters (e.g. PP does not occur)
- all n-grams (n = 2, 3, ...) are unique
- on a given line, all characters are unique
- no identical adjacent characters across lines within a distance of 8 positions.
- 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
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This chart uses all the letters of the alphabet and is typset using my Snellen font redesign.
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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).
- no more than 19 instances of any character and no fewer than 15
- no double characters (e.g. AA does not occur)
- no more than 7 repeats of any 2-gram
- no more than 4 repeats of any 3-gram
- no more than 2 repeats of any 4-gram or 5-gram
- for a given line, the characters at the same position in the previous 2 lines are different
- chart starts with start codon ATG
- 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
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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!
Charts ahoy!
Z KE CHG XVRM YTWUS JQFINB EZAOXLD NHKVCUGF SWRMIAZP DBTOJYXE FZHLNUKA IVGMYCWR
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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.
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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.
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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.
44 intriguing and perhaps mysterious mathematical symbols ranging from common equality `=` to the esoteric normal subgroup `\triangleleft`.
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.
Convolutional neural networks
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry. – Richard Feynman
Following up on our Neural network primer column, this month we explore a different kind of network architecture: a convolutional network.
The convolutional network replaces the hidden layer of a fully connected network (FCN) with one or more filters (a kind of neuron that looks at the input within a narrow window).
Even through convolutional networks have far fewer neurons that an FCN, they can perform substantially better for certain kinds of problems, such as sequence motif detection.
Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Convolutional neural networks. Nature Methods 20:.
Background reading
Derry, A., Krzywinski, M. & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.
Neural network primer
Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon
In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.
Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.
We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.
Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.
Background reading
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.
Cell Genomics cover
Our cover on the 11 January 2023 Cell Genomics issue depicts the process of determining the parent-of-origin using differential methylation of alleles at imprinted regions (iDMRs) is imagined as a circuit.
Designed in collaboration with with Carlos Urzua.
Akbari, V. et al. Parent-of-origin detection and chromosome-scale haplotyping using long-read DNA methylation sequencing and Strand-seq (2023) Cell Genomics 3(1).
Browse my gallery of cover designs.
Science Advances cover
My cover design on the 6 January 2023 Science Advances issue depicts DNA sequencing read translation in high-dimensional space. The image showss 672 bases of sequencing barcodes generated by three different single-cell RNA sequencing platforms were encoded as oriented triangles on the faces of three 7-dimensional cubes.
More details about the design.
Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9.
Browse my gallery of cover designs.
Regression modeling of time-to-event data with censoring
If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber
In a follow-up to our Survival analysis — time-to-event data and censoring article, we look at how regression can be used to account for additional risk factors in survival analysis.
We explore accelerated failure time regression (AFTR) and the Cox Proportional Hazards model (Cox PH).
Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Regression modeling of time-to-event data with censoring. Nature Methods 19:1513–1515.