After finding a typographic portrait of Christopher Hitchens, created out of Gill Sans letters by Miles Chic at Capilano University, I thought to resurrect software I wrote a long time ago that converts images into letters and expanding traditional ASCII art by using
The representation of images by characters—ASCII art—has a long history. ASCII art extends the emoticon (or smiley) to represent a larger piece of work. Typically, the works use a fixed-space font (e.g. Courier), originally designed for display on a terminal. Despite the sophistication of computer graphics today, ASCII art continues to have a strong following with new work continually added to public online galleries.
Photos and paintings can be ASCIIfied using a tone-based approach and automated methods exist to do this (Paul D. O’Grady and Scott T. Rickard (2008) Automatic ASCII Art Conversion of Binary Images Using Non-Negative Constraints).
Many artists generate new creations, exclusive to the medium. Typically this kind of ASCII art is based on the interpretation of structure rather than tone—this method has also been automated (Xuemiao Xu, Linling Zhang, Tien-Tsin Wong (2010) Structure-based ASCII Art).
I have written code to generate ASCII art from images by using proportional spaced fonts.
Let's see how these methods work on a real image. Many ASCII art Mona Lisa versions exist. Below, I render the Mona Lisa with Pragmata, Gotham Book and 8 weights of Gotham.
Two-tone shapes like the S in the figure above require selecting characters that match the structure of the image. (e.g. "|" matches vertical lines). For a given character and image position there are four distinct match possibilities—a combination of whether the character and image have a signal at a position. I show this in the figure below.
By maximizing scores derived from matches (s1, s3) and minimizing any penalties (s2, s4), a character is identified based on maximal coverage of the image region and minimum coverage of areas that are blank.
When proportional text is used, edges are better approximated, such as in the Homer Simpson example below which uses Gotham Book.
Images that are not two-tone require that we match both structure and tone. Structure is approximated by the choice of character, while tone by choice of font weight. To select the best character based on tone, the character's average tone is compared to the average tone of the section of the image to which it is being compared.
It is possible to combine both structure and tone metrics in character selection. Below is an example of how an image with both tone and structure is interpreted as the tone and structure score weights are varied. The balance between these two metrics can be very hard to find—it greatly depends on the image. Tone-based mapping works well when font size is small and the image is viewed from larger distance—in this case, characters play the role of individual pixels with varying brightness. Structure-based mapping works with larger type and closer viewing distance.
Continuous tone bitmaps are an idea application of multi-font ASCII art—images no longer need to be thresholded or dithered.
ASCII art is generated by dividing the image into a grid and finding the letter (the choice of characters is often expanded to include punctuation) that best matches the grid section. Typically, for each grid the entire set of allowable characters is sampled. Instead, we can limit the choice of character by successively sampling from a fixed string.
rendered with the fixed string "monalisa" using 8 weights of Gotham.
Things get even more interesting when the text is angled.
The image can be textured with multiple layers of ASCII art. In the example below, four layers of text are used, each with a different font size.
Instead of varying size, the angle of the text can be changed among layers. This results in a pattern reminiscent of a halftone.
An image can be asciified several times, with each iteration the asciified output of the previous step used as input for the next. At each step, the font size should be reduced to s → √s.
Today is the day and it's hardly an approximation. In fact, `22/7` is 20% more accurate of a representation of `\pi` than `3.14`!
Time to celebrate, graphically. This year I do so with perfect packing of circles that embody the approximation.
By warping the circle by 8% along one axis, we can create a shape whose ratio of circumference to diameter, taken as twice the average radius, is 22/7.
Regression can be used on categorical responses to estimate probabilities and to classify.
The next column in our series on regression deals with how to classify categorical data.
We show how linear regression can be used for classification and demonstrate that it can be unreliable in the presence of outliers. Using a logistic regression, which fits a linear model to the log odds ratio, improves robustness.
Logistic regression is solved numerically and in most cases, the maximum-likelihood estimates are unique and optimal. However, when the classes are perfectly separable, the numerical approach fails because there is an infinite number of solutions.
Altman, N. & Krzywinski, M. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.
Altman, N. & Krzywinski, M. (2016) Points of Significance: Regression diagnostics? Nature Methods 13:385-386.
Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.
Genomic instability is one of the defining characteristics of cancer and within a tumor, which is an ever-evolving population of cells, there are many genomes. Mutations accumulate and propagate to create subpopulations and these groups of cells, called clones, may respond differently to treatment.
It is now possible to sequence individual cells within a tumor to create a profile of genomes. This profile changes with time, both in the kinds of mutation that are found and in their proportion in the overall population.
Clone evolution diagrams visualize these data. These diagrams can be qualitative, showing only trends, or quantitative, showing temporal and population changes to scale. In this Molecular Cell forum article I provide guidelines for drawing these diagrams, focusing with how to use color and navigational elements, such as grids, to clarify the relationships between clones.
Krzywinski, M. (2016) Visualizing Clonal Evolution in Cancer. Mol Cell 62:652-656.
Limitations in print resolution and visual acuity impose limits on data density and detail.
Your printer can print at 1,200 or 2,400 dots per inch. At reading distance, your reader can resolve about 200–300 lines per inch. This large gap—how finely we can print and how well we can see—can create problems when we don't take visual acuity into account.
The column provides some guidelines—particularly relevant when showing whole-genome data, where the scale of elements of interest such as genes is below the visual acuity limit—for binning data so that they are represented by elements that can be comfortably discerned.
Krzywinski, M. (2016) Points of view: Binning high-resolution data. Nature Methods 13:463.