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These typefaces are really mysterious

 


The origin of the verb “puzzle” is unknown, embarrassing, confusing, embarrassing, and embarrassing. Martin Demain, an artist at the Massachusetts Institute of Technology, said: “”

His son, Eric Demain, a computer scientist at MIT, also agreed. “It’s a self-describing etymology,” he said.

The father and son duo are best known for their mathematical studies of paper origami. Curved crease engraving A pleated paper swirl loop that resembles intergalactic alternating current. Curved origami Bauhaus classic specimens of the late 1920s begin as automatically twisted circular pieces of paper. Folding along the concentric circles creates a saddle curve. Demaines’ three works, “Calculation origami,” “Is part of the 2008,” and “Design and the Elastic Mind,” were held at the Museum of Modern Art in New York and are now a permanent collection.

However, recently, Demaines has focused on “algorithm puzzle fonts,” which are a series of mathematically inspired typefaces and puzzles. The main application is fun. One font, a homage to mathematicians and jugglers, Ronald Graham, who died in 2020, draws his character from the pattern of movement traced by a ball thrown into the air.

Another font proposed by computer scientist Donald Knuth (almost all fonts involve collaborators). A distinctive feature is that all letters are “anatomically chopped and rearranged into 6 x 6 squares.

In the 2015 paper “Enjoy Fonts: Algorithmic Typography,” “Demaines explained their motives.” Scientists use fonts every day to express their research in the written language, but the font itself is the research ( If you are telling the spirit of). What if writing the text, not just the text itself, draws the reader into science? “”

Inspired by theorems or unsolved problems, fonts (and the messages they create) can usually only be read after solving a related puzzle or set of puzzles.

For example, take a look at the new fonts in the collection that debuted today. Sudoku Fonts .. Inspiration was born in the fall of 2019 when Eric Demain co-taught the “Basics of Programming” course (with computer scientist Slini Devadas). In class, Dr. Demaine and his 400 freshmen and sophomores have programmed the Sudoku solver with code to solve Sudoku puzzles. That day, Dr. Demain’s father attended a lecture on whether he could create a Sudoku-based font, a puzzle-based font that reveals the character with his own solution, with half the care. .. I thought. Of the alphabet.

After experimenting with different possibilities, Demaines designed a Sudoku puzzle font that works as follows: Start with one of the Sudoku puzzles and solve it. Then draw a line connecting the longest path of the square to a series of numbers (only the squares adjacent to the edges, not diagonally, in ascending or descending order). Lines draw the shape of letters on the grid of the puzzle. A series of Sudoku resolved in this way can reveal the following message:

An entire suite of puzzle fonts with varying degrees of interactivity is available. On Dr. Demaines’s website, Demaines manually designed the shape of the letters, but used a computer to generate a Sudoku puzzle that embeds the letters.

“It was still difficult to design a character that could solve the puzzle, and we didn’t have to add a drift connection to the longest path,” said Dr. Demain. “This was a very difficult font to design for both humans and computers.”

Math + art = fun

Demaines began experimenting with this puzzle font at the turn of the century using anatomical puzzles. This is a puzzle that slices one shape, a polygon, and reconstructs it into another geometry. Their motive was the issue raised by British and Australian engineer and amateur mathematician Harry Lindgren in 1964. Is it possible to subdivide and rearrange all the letters of the alphabet to form a square?

In 2003, the previous job, Demaines Proven Yes, it was certainly possible, and they announced the results. (Puzzle fonts usually come with a corresponding research treatise.) This first advance was only in the sense that Demaines had been confused about how to design fonts for some time. We made the task even more mysterious by adding more criteria. It needed “hinge anatomy”, not just an anatomical font. This is a special kind of anatomy in which the pieces are hinged at the apex to form a closed chain. In this case, move to all other letters of the alphabet, not just the square you want.

They have succeeded in exploring the mathematics of “polyforms”, which are shapes created from multiple copies of polygons such as triangles. More precisely, they used a polyform with the unlikely name “polyabolo” (popular by Scientific American math columnist Martin Gardner). Polyaboro is made up of congruent right isosceles triangles. The square can be cut into two right isosceles triangles. Then these two triangles are divided into four right-angled isosceles triangles, four triangles in 8, 8 in 16, 16 in 32, 32 in 64, 64 in 128, and so on. It will be split. it can.

In this way, Demaines created the anatomical font. All letters of the alphabet are divided into 32 triangles (labeled “32-Aboro”) and can be rearranged into 4-by-4 squares or other letters. However, the desired outcome hinged anatomy could be converted from one connected triangular chain character to another character Each character had to be decomposed into 128 triangular fragments (to “128 Aboro”) ).

Demaines recalled this exercise in an email and said: .. It was to aim. shape). “”

Deadlocked philosophy

Twenty years later, their humble beginnings sprouted in a wonderfully fun font house with a variety of artistic media. Glass sticks, string art, coins.

Think of a tiling font: each character is “displayed side by side”. This means, as Demaines explains, “with an infinite number of copies of that one shape, you can fill 2D without leaving any gaps between the tiles.” Ideal for bathroom remodeling.

With the conveyor belt font, each letter is formed by a closed loop of the conveyor belt that bends around a strategically placed wheel. (Font names are intentionally spelled “conveyor” rather than “conveyor” to “send” letters and words.)

The Conveyor Belt Font was inspired by an open question posed by the Spanish mathematician Manuel Averanas in 2001. If there are multiple wheels or discs of the same size that do not overlap in two dimensions, they are all taut conveyor belts and the belts touch. Are all the wheels crossing themselves?

Demaines got stuck trying to solve this problem. They were distracted by designing the font. “It has always been an important part of our philosophy,” Demain said. “If you’re stuck with a problem, I want to find an artistic way to express it.”

Demaines also found that puzzles are a good way to start the fun of formal math for beginners. Checker Fonts When Spencer Congero, a graduate student in computer science at the University of California, San Diego, came across this idea, Spiral Galaxy Fonts (based on a Japanese pencil and paper puzzle of the same name. The unique solution to the puzzle is letters. Is a student at Central Bucks West High School in Doylestown. Pennsylvania, and the US World Puzzle Championship team. ..

Puzzle fonts were the gateway to Anderson’s mathematical research. He is currently an undergraduate student studying mathematics at MIT For the Demaines. This kind of collaboration is the reason for the celebration. The other has “collapsed” into the world of theoretical computer science.

Creative constraints

Given its reputation for origami, Demaines naturally created some fonts that riff the nuances of origami. Origami Maze Fonts, Simple Folding & Cut Fonts, Folding & Punch Fonts Folding Fonts If Not Possible ..

Demaines also decided to create a minimal font that would only require one change.

For simplicity, we’ve added restrictions to keep unresolved fonts unreadable. The characters should be unreadable before they can be folded. In fact, most of these typefaces are based on similar constraints. Demaines likes to make tasks difficult, but they don’t do it unreasonably. They don’t want a lot of freedom or flexibility because attractiveness matters, but they do want the task to be achievable.

Use these parameters to use a one-fold silhouette font. The silhouette element borrows from the 1900s “Rabbit Silhouette Puzzle” and stacks 5 cards with various animal cutouts to create a rabbit silhouette. Folded silhouette fonts also work. Imagine a transparent sheet with black markings.

The vertical crease in the center encourages the sheet to fold in half (from right to left, like turning the pages of a book).

And to my surprise, the text was revealed!

The strip folding font folds a series of characters from a long piece of paper. The limitation here was that all characters had to be folded using horizontal, vertical, and diagonal creases.

Font physics

Last fall, Demaines announced the Tetris font. This is a continuation of research on the computational complexity of iconic Falling-block video games. (In 2002, Eric Demain said in honor of the Tetris Master Harvard University Tetris Association’s “Intellectual Contribution to Tetris Art” in his basic treatise “It’s Difficult to Estimate Tetris.”)

The results of the new results are as follows: By playing the offline version of Tetris (the player has the existing complete information about the ID and the order of the pieces to drop), the game proved to be “NP-complete”. That is, there is no efficient solution algorithm, even with 8 columns or 4 rows. In fact, as Dr. Demain explains on his website, NP-completeness means “can the board survive or be cleared given the initial configuration of the board and board set?” It is difficult to determine by calculation. n Coming works. “”

Initially, the creative limitation of this font was that each character was built as a stack of one copy of all seven Tetris shapes. Later, Demaines realized that it was appropriate to animate the font with the formed characters, like in-game pieces. Therefore, each piece placed was supported by the previous piece without extreme overhangs and had to follow “Tetris physics”. This required a slight redesign using computer tools (“BurrTools”) to assemble the desired shape from the basic unit parts.

“When we humans got stuck in finding a good solution, we put some of the forms we were trying into BurrTools, which helps guide our search.” Dr. Demaine said. Said. The “Q” and “M” are one of the last placed letters.

Finally, try to understand all the fonts just released today. This was inspired by the eye chart with “Es” on every row. In the context of mathematical fonts, the letter “E” is the so-called “canonical form”. You can fold all letters of the alphabet into “E” and “E” into all letters. That is, in the end, all characters can be collapsed into all other characters. (The natural standard form of protein chains that fold into various shapes is a helix.)

So if this article is written in Everything Font and each character has a different character crease pattern (folding procedure), here is another encoded article.

These typefaces are really mysterious

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