# [Visions of Type](http://mkweb.bcgsc.ca/typography/eyecharts.mhtml) | ![snellenmk.poster.01](https://user-images.githubusercontent.com/25581533/93721966-e8e71500-fb82-11ea-8613-8f7563c0ba5a.png) | ![snellenmk.poster.03](https://user-images.githubusercontent.com/25581533/93723397-ce666900-fb8d-11ea-986b-c5a1145d0eff.png) | ![snellenmk.poster.02](https://user-images.githubusercontent.com/25581533/93721968-eb496f00-fb82-11ea-97e1-30ec439b792f.png) | |------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------| | ▲ SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. | ▲ SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. | ▲ SnellenMK optotype font. Uppercase, lowercase and symbols to test your eyes. | # Eyes On the Universe These typographical posters are designed after the style of the [Snellen Chart](https://en.wikipedia.org/wiki/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](https://fineartamerica.com/profiles/martin-krzywinski?tab=artworkgalleries&artworkgalleryid=714111). ## Optotypes Symbols on such charts are known as optotypes. Fonts by Andrew Howlett exist whose glyphs conform to the properties of optotypes: [Snellen font](http://mkweb.bcgsc.ca/typography/fonts/snellen-font.zip) and [Sloan font](http://mkweb.bcgsc.ca/typography/fonts/sloan-font.zip). However, some of the characters in the Snellen font file are a little oddly shaped—I provide my [redesign of the Snellen font](http://mkweb.bcgsc.ca/snellen-optotype-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](http://mkweb.bcgsc.ca/snellen-optotype-font/) or [Monotype's Rockwell](https://www.fonts.com/font/monotype/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](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2030)) 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](https://render.githubusercontent.com/render/math?math=\large%206%20/%206) (or ![20/20](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2020)) [visual acuity](https://en.wikipedia.org/wiki/Visual_acuity). This corresponds to a letter size of ![(2π/360) × (5/60) × 6 = 8.727mm = 24.74pt](https://render.githubusercontent.com/render/math?math=\huge%20\frac{2\pi}{360}%20\times%20{5%20\over%2060}%20\times%206%20=%208.727%20mm%20=%2024.74%20pt) ``` latex \frac{2\pi}{360} \times {5 \over 60} \times 6 = 8.727 mm = 24.74 pt ``` The Snellen optotypes are designed on a ![5 × 5](https://render.githubusercontent.com/render/math?math=\large%205%20\times%205) grid and have a [fascinating history](https://gizmodo.com/examining-the-typographic-history-of-eye-charts-1732823179). For design, [Rockwell](https://www.fonts.com/font/monotype/rockwell) and [Lubalin Graph](https://www.linotype.com/1488211/itc-lubalin-graph-family.html) can be used to approximate Snellen, though these fonts lack the grid structure of the optotypes. ![optotypes](https://user-images.githubusercontent.com/25581533/93724093-ac6fe500-fb93-11ea-921a-8defb47c8745.png) ▲ Snellen optotypes are designed on a ![5 × 5](https://render.githubusercontent.com/render/math?math=\large%205%20\times%205) grid. At a viewing distance of `6 m` (`20 ft`) each letter on the ![6/6](https://render.githubusercontent.com/render/math?math=\large%206%20/%206) (or ![20/20](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2020)) 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. ### snellen optotype font My redesign of Andrew Howlett's Snellen optotype font. Read about [redesign process](http://mkweb.bcgsc.ca/snellen-optotype-font/)—which reinterprets some of the characters and adds lowercase. You can [download both versions of the font](http://mkweb.bcgsc.ca/snellen-optotype-font/). ![snellen-optotype-font-v07.1-01](https://user-images.githubusercontent.com/25581533/93723138-93633600-fb8b-11ea-86a0-c4922a404394.png) ▲ Snellen optotypes are designed on a ![5 × 5](https://render.githubusercontent.com/render/math?math=\large%205%20\times%205) grid. At a viewing distance of `6 m` (`20 ft`) each letter on the ![6/6](https://render.githubusercontent.com/render/math?math=\large%206%20/%206) (or ![20/20](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2020)) acuity line must be `8.727 mm` (`24.47 pt`) ## The Posters ### Conventional Snellen charts These Snellen charts include acuity lines from ![20/200](https://render.githubusercontent.com/render/math?math=\large%2020%20/%20200) to ![20/10](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2010). The charts should be printed at a physical size of ![16" × 24"](https://render.githubusercontent.com/render/math?math=\large%2016%27%27%20\times%2024%27%27) (![1150 pt × 1725 pt](https://render.githubusercontent.com/render/math?math=\large%201150%20pt%20\times%201725%20pt). At this size, the characters on the ![20/20](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2020) 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](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2030) and ![20/20](https://render.githubusercontent.com/render/math?math=\large%2020%20/%2020) 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](https://render.githubusercontent.com/render/math?math=\large%20d), measure the length of these lines, ![L](https://render.githubusercontent.com/render/math?math=\large%20L) (in inches) and use ![d = 6 × L/8](https://render.githubusercontent.com/render/math?math=\huge%20d%20=%206%20\times%20L%20/%208) ``` latex d = 6 \times L / 8 ``` For example, if I print this chart to fit onto an ![8.5" × 11"](https://render.githubusercontent.com/render/math?math=\large%208.5%27%27%20\times%2011%27%27) page, these lines are `3.47"`. Thus, my smaller chart should be viewed from ![6 × 3.47/8 = 2.60m](https://render.githubusercontent.com/render/math?math=\large%206%20\times%203.47%20/%208%20=%202.60%20m)(`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. ![snellen-chart-efp-01](https://user-images.githubusercontent.com/25581533/93724407-4f296300-fb96-11ea-84f1-f89c7355105b.png) ▲ 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](https://render.githubusercontent.com/render/math?math=\large%2016%20in%20\times%2024%20in). ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-9-character-martin-krzywinski.html)) #### 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 ``` ![snellen-chart-alphabet-01](https://user-images.githubusercontent.com/25581533/93724818-e7751700-fb99-11ea-83be-9b689da13951.png) ▲ 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](https://render.githubusercontent.com/render/math?math=\large%2016%20in%20\times%2024%20in). ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-full-alphabet-martin-krzywinski.html)) #### 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 ``` ![snellen-chart-genetic-sequence-01](https://user-images.githubusercontent.com/25581533/93724849-3b7ffb80-fb9a-11ea-948e-210085241d37.png) ▲ 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](https://render.githubusercontent.com/render/math?math=\large%2016%20in%20\times%2024%20in). ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-genetic-sequence-martin-krzywinski.html)) The best alignments of this chart's sequence are to fungus (*Leptosphaeria maculans lepidii*, ![35/42](https://render.githubusercontent.com/render/math?math=\large%2035/42), `83%`) and a tapeworm (*Diphyllobothrium latum*, ![24/26](https://render.githubusercontent.com/render/math?math=\large%2024%20/%2026), `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 ``` ![snellen-chart-nautical-flags](https://user-images.githubusercontent.com/25581533/93722374-e2a66800-fb85-11ea-8ee6-8b79e60eda54.png) ▲ A technically accurate Snellen chart using the nautical flag alphabet rendered as optotypes. Print at ![16 in × 24 in](https://render.githubusercontent.com/render/math?math=\large%2016%20in%20\times%2024%20in). ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-nautical-flags-martin-krzywinski.html)) 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](https://render.githubusercontent.com/render/math?math=\large%205%20\times%205) optotype grid. The checker of `N` is now a ![5 × 5](https://render.githubusercontent.com/render/math?math=\large%205%20\times%205) 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. ![nautical-flag-optotypes-01](https://user-images.githubusercontent.com/25581533/93725004-3ff8e400-fb9b-11ea-9370-ac56cadb9852.png) ▲ Snellen optotypes for the nautical flag alphabet. ### Eyes on the elements Elements are sorted in order of abundance. The numbers on the left show the max and min ![−log_10](https://render.githubusercontent.com/render/math?math=\large%20-\log_10) abundance of the elements listed on a given line. For example, ![3.0/3.3](https://render.githubusercontent.com/render/math?math=\large%203.0%20/%203.3) 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](http://mkweb.bcgsc.ca/typography/elements.parsed.universe.txt) ([original source](https://periodictable.com/Properties/A/UniverseAbundance.v.log.html), `83 elements`) and [table of abundance of elements in the body](http://mkweb.bcgsc.ca/typography/elements.parsed.body.txt) ([original source](https://en.wikipedia.org/wiki/Composition_of_the_human_body), `60 elements`). These have been parsed from the original sources and give the ![−log_10](https://render.githubusercontent.com/render/math?math=\large%20-\log_10) abundance for various elements. ![snellen-chart-elements-universe](https://user-images.githubusercontent.com/25581533/93725109-0e344d00-fb9c-11ea-814a-fdf4ac45db7b.png) ▲ Snellen Chart of abundance of the elements in the universe. ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-chemical-abundance-in-universe-martin-krzywinski.html)) ![snellen-chart-elements-body](https://user-images.githubusercontent.com/25581533/93725118-14c2c480-fb9c-11ea-8920-4866bbe75ff4.png) ▲ Snellen Chart of abundance of the elements in the human body. ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-chemical-abundance-in-human-body-martin-krzywinski.html)) ### Eyes on physical constants 44 of the most interesting physical constants ranging from the very large (Planck temperature ![T_p = 1.4 × 10^32 K](https://render.githubusercontent.com/render/math?math=\large%20T_p%20=%201.4%20\times%2010^32%20K)) to the very small (cosmological constant ![Λ = 1.19 × 10^−52 m^−2](https://render.githubusercontent.com/render/math?math=\large%20\Lambda%20=%201.19%20\times%2010^{-52}%20m^{-2})). You can [download the table of constants and their values](http://mkweb.bcgsc.ca/typography/physical.constants.txt). ![snellen-chart-physical-constants](https://user-images.githubusercontent.com/25581533/93725231-f4dfd080-fb9c-11ea-856f-49928fc96fed.png) ▲ Snellen Chart of physical constants. ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-physical-constants-martin-krzywinski.html)) ### Eyes on mathematical symbols 44 intriguing and perhaps mysterious mathematical symbols ranging from common equality ![=](https://render.githubusercontent.com/render/math?math=\large%20=) to the esoteric normal subgroup ![◃](https://render.githubusercontent.com/render/math?math=\large%20\triangleleft). ![snellen-chart-math](https://user-images.githubusercontent.com/25581533/93725261-2ce71380-fb9d-11ea-881c-f3080170a7e5.png) ▲ Snellen Chart of mathematical operators and symbols. ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-mathematical-symbols-martin-krzywinski.html)) ### 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](https://en.wikipedia.org/wiki/Snellen_chart), which is limited to the `10` [Sloan letters](https://en.wikipedia.org/wiki/Sloan_letters) `C`, `D`, `E`, `F`, `L`, `N`, `O`, `P`, `T`, `Z`. ![snellen-chart-braille](https://user-images.githubusercontent.com/25581533/93725339-0a092f00-fb9e-11ea-8881-767a9ed1b06b.png) ▲ Snellen Chart typeset in Braille. ([BUY ARTWORK](https://fineartamerica.com/featured/snellen-chart-braille-martin-krzywinski.html)) ![snellen-chart-braille-2](https://user-images.githubusercontent.com/25581533/93725341-0bd2f280-fb9e-11ea-9e4b-69b8eea709fa.png) ▲ Snellen Chart typeset in Braille. Variant #2. ([BUY ARTWORK](https://fineartamerica.com/featured/1-snellen-chart-braille-martin-krzywinski.html)) ![snellen-chart-braille-3](https://user-images.githubusercontent.com/25581533/93725342-0d041f80-fb9e-11ea-9269-e5f869ffa485.png) ▲ Snellen Chart typeset in Braille. Variant #3. ([BUY ARTWORK](https://fineartamerica.com/featured/2-snellen-chart-braille-martin-krzywinski.html)) # LICENSE © 1999–2020 [Martin Krzywinski](http://mkweb.bcgsc.ca/) | [contact](martink@bcgsc.ca)