Erik and martin demaine, a father-and-son team of “algorithmic typographers,” accept confected an all suite of mathematically inspired typefaces.

the verb “puzzle” — to bewilder or confuse, dazzle or bemuse — is of hidden cause. “that bark of fits,” said martin demaine, an artist in abode at the massachusetts appoint of technology. “it’s a bewilder where the account ‘puzzle’ comes from.”

his son, erik demaine, an m.i.t. computer scientist, acknowledged. “it’s a self-describing etymology,” he said.

the father-son duo is most celebrated for mathematical investigations into paper folding, with “curved-crease sculptures” — swirling loops of pleated paper that resemble intergalactic interchanges. curved origami dates to recent 1920s bauhaus; a classic illustration starts as a round piece of paper, which, when folded along concentric circles, automatically twists into a burden arcuate. the demaines’ trio of pieces, “computational origami,” was behalf of the 2008 “design and the alterable mind” broach at the museum of existent wile in novel york and now resides in its permanent assemblage.

these days, however, the demaines are more focused on “algorithmic bewilder fonts,” a suite of mathematically inspired typefaces that are likewise puzzles. the main study is jest. single font, a al to the mathematician and juggler ron graham, who died in 2020, draws its letters from the patterns of movement traced by balls thrown into the cast during juggling tricks.videothe juggling font, by erik demaine and martin demaine.

another font, proposed by the computer scientist donald knuth (almost entire fonts complicate collaborators), has as its distinguishing prominent that entire letters can continue “dissected” — scarify into pieces and rearranged — into a 6-by-6 square.imagethe dissection font.credit…erik demaine, martin demaine, donald e. knuth, yushi uno

in a 2015 paper, “fun with fonts: algorithmic typography,” the demaines explained their motivations: “scientists advantage fonts every day to direct their elaboration through the written account. barring what if the font itself communicated (the activity of) the research? what if the fashion text is written, and not equitable the text itself, engages the reader in the science?”

inspired by theorems or accessible problems, the fonts — and the messages they adjust — can usually continue decipher merely behind solving the akin bewilder or course of puzzles.

take, for instance, a novel font in their assemblage that debuts today: the sudoku font. the afflatus came in the decline of 2019, when erik demaine co-taught the method “fundamentals of programming” (with the computer scientist srini devadas). during single class, appropriate. demaine and his 400 freshmen and sophomores programmed a sudoku solver — they wrote code that solved a sudoku bewilder. appropriate. demaine’s elder sat in on the lecture that day, and while half-paying observation mr. demaine mused almost whether it might continue practicable to wage a font based on sudoku — that is, based on the puzzles whose choice solutions would somehow communicate letters of the alphabet.

after playing about with different possibilities, the demaines adapted a sudoku bewilder font that works as follows: first, begin with single of their sudoku puzzles and explain it. next, educe a cord connecting the longest course of squares with arranged numbers (ascending or descending; barring merely edge-adjacent squares, not diagonal). that cord draws the adapt of a communication within the grid of the bewilder. a course of sudokus thus solved can communicate a message, approve so: videothe sudoku font, by erik demaine and martin demaine.

the all suite of bewilder fonts is available, with varying degrees of interactivity, on appropriate. demaine’s website. the demaines hand-designed the communication shapes, barring used a computer to beget the letter-embedding sudoku puzzles.

“it was arduous to propose letters that calm enabled the bewilder to continue solvable, and without adding additional depart connections to the longest path,” appropriate. demaine said. “this was altogether a toilsome font to design, twain for the anthropological and the computer.”math + wile = fun

the demaines began this puzzle-font experiganza about the act of the century with a dissection bewilder — a bewilder whereby single shape, or polygon, is sliced up and reassembled into other geometric shapes. their motivation was a problem posed in 1964 by harry lindgren, a british-australian engineer and amateur mathematician: can every communication of the alphabet continue dissected into pieces that rearrange to arrange a square?

in 2003, structure on antecedent work, the demaines proved that, yes, certainly it was possible, and they published the conclusion. (typically, a bewilder font comes with a corresponding elaboration paper.) this chief escapade was a bewilder merely in the apprehension that the demaines were perplexed for a while almost how to propose the font. and they made the brave more puzzling by adding an extra criterion: they wanted not only a dissection font, barring a “hinged dissection” — a appropriate bark of dissection whereby the pieces are collateral (hinged) at their vertexes, forming a closed chain that rearranges, in this instance not merely into the desired square barring likewise into every other communication of the alphabet.

they succeeded in their quest by deploying the mathematics of “polyforms,” shapes made from multiple copies of a polygon, such as a triangle. more precisely, they used a polyform with the improbable appellation “polyabolo” (popularized by martin gardner, who was a mathematics columnist for scientific american). a polyabolo is made from congruent claim isosceles triangles. a square can continue scarify into two claim isosceles triangles; and those two triangles can in act continue scarify into four claim isosceles triangles, and those four triangles into eight, and those eight into 16, 16 into 32, 32 into 64, 64 into 128, and so forth.

by this method, the demaines created their hinged-dissection font. every communication of the alphabet is dissected into 32 triangles (rendering it a “32-abolo”) that can continue rearranged into a 4-by-4 square, or any other communication. barring achieving the desired hinged dissection — a collateral chain of triangles that can morph from single communication into any other — required that each communication continue dissected into 128 triangular pieces (making it a “128-abolo”).imagea 128-piece hinged dissection.credit…erik demaine and martin demaine

reflecting on this application in an email, the demaines said: “the jest for us was combining wile and math together, aiming for actual propose (recognizable as letters and looking steady transverse the alphabet) within arduous mathematical constraints (fixed area and working with polyabolo shapes).”imagethe hinged-dissection font.credit…erik demaine and martin demainethe philosophy of getting stuck

twenty years on, those low beginnings accept sprouted into a feigned jest house of fonts, with finished media as varied as rods of glass, string wile and coins.

consider the tiling font: each communication “tiles the plane,” meaning, as the demaines explain, “that infinitely abundant copies of that single adapt can replenish two dimensions without leaving any gaps between the tiles.” absolute for a bathroom resurrection.imagethe tiling font.credit…erik demaine, martin demaine, scott kim, yushi uno

with the conveyer belt font, each communication is formed by the closed loop of a conveyor belt that curves about strategically placed wheels. (the font appellation is intentionally spelled “conveyer” rather than “conveyor,” as the font “conveys” letters and words.)imagethe conveyer belt font.credit…erik demaine, martin demaine, belén palop

the conveyer belt font was prompted by a still-unsolved problem posed in 2001 by the spanish mathematician manuel abellanas: if there are distinct two-dimensional and nonoverlapping wheels, or disks, of peer size, can they entire continue wrapped (connected) with a taut conveyor belt, such that the belt touches entire the wheels barring doesn’t intersect itself?

the demaines tried to explain this problem and got stuck. they raving themselves by designing the font. “that’s ever been an momentous behalf of our philosophy,” mr. demaine said. “if we achieve stuck on a problem, we approve to ascertain an finished fashion to delineate it.”

the demaines likewise ascertain that puzzles are a accurate fashion to initiate newcomers into the jest of affected mathematics. the checkers font (in which the letters are formed from paths of jumping moves) came into essence when spencer congero, a computer comprehension graduate student at the university of california, san diego, got in affect with the idea. the spiral galaxies font (based on the japanese pencil-and-paper bewilder of the identical name; choice solutions to puzzles arrange letters) was a collaboration with walker anderson, then a student at accessible bucks west tall school in doylestown, pa., and a constituent of the usa world bewilder championship team.

the bewilder font was mr. anderson’s gateway to mathematical research; now he’s an undergrad studying math at m.i.t. for the demaines, these sorts of collaborations are occasion for celebration: single more peculiar successfully “corrupted” into the world of hypothetical computer comprehension.creative constraint

given their reputation with origami, the demaines accept naturally created a manifold fonts riffing on the nuances of folding, including the origami maze font, the shallow double & scarify font, the double & perforate font and an impossible folding font.

the demaines likewise decided, for a change, to beget a minimalistic font requiring merely a one double.

lest that plainness wage the unsolved font too shallow to read, they appended a restriction: the letters must continue illegible antecedently folding. most of their typefaces, in fact, are based about alike constraints. the demaines approve to wage the business arduous barring not preposterously so; they don’t deficiency too abundant freedom or flexibility, whereas the attract is in the challenge, barring they do deficiency the business to continue attainable.

with these parameters, they devised the one-fold silhouette font. the silhouette atom borrows from a 1900-era “rabbit silhouette puzzle,” in which five cards with cutouts of different animals stack up to accomplish the silhouette of a rabbit. the one-fold silhouette font works in a alike fashion. apprehend a clear sheet, with black markings: imagethe one-fold silhouette font.credit…erik demaine and martin demaine

the accessible vertical corrugate invites you to double the sheet in half (from claim to left, as if you were turning the page of a book).

and surprise, the text is revealed!image

with the strip-folding font, a consequence of letters is folded from a pant bare of paper — the constraint here was that every communication had to continue foldable using merely horizontal, vertical and diagonal folds.imagethe strip-folding font.credit…erik demaine and martin demainefont physics

last fall, the demaines published their tetris font, which is a concatenation of their studies into the computational intricacy of the iconic falling-block video amusement. (in 2002 erik demaine was conferred the address of “tetris master” by the harvard tetris society, in respect of his “intellectual toll to the wile of tetris,” for a foundational paper, “tetris is hard, equable to abut.”)

the conclusion of the novel conclusion is this: they accept proved, in playing the offline account of tetris (wherein the player has full news in allege almost the convertibility and adjust of pieces that accomplish drop) that the amusement is “np-complete” — aim that no productive answer algorithm exists, equable with as manifold as eight columns or four rows. and more practically, as appropriate. demaine graphic on his website, np-completeness instrument “it’s computationally intractable to appearance disembowel whether you can survive, or sonorous the board, given an initial carpet conformation and a consequence of n pieces to come.”

initially, the poetical constraint for this font was that each communication continue constructed as a stacking of single example of entire seven tetris shapes. then the demaines realized it would continue neat to inspire the font, with letters dropping into construction approve pieces in the amusement — so that each piece placed likewise had to continue supported by the antecedent pieces, with no distant overhangs, thus obeying “tetris physics.” this necessitated a atom of redesign, sometimes with the aid of a computer dupe (“burrtools”) that assembled desired shapes from basic item pieces.

“when us humans got stuck finding a actual solution, we’d put some of the shapes we’d been trying into burrtools, and it would aid conduct our search,” appropriate. demaine said. “q” and “m” were amidst the abide letters to decline into assign.videothe tetris font, by erik demaine and martin demaine.

finally, aim to gauge everything font, likewise equitable released today into the chimerical. it was inspired by those eye charts with “es” on every cord. in the mathematical font context, the communication “e” is what’s denominated a “canonical form” — every communication of the alphabet can continue folded into an “e,” and “e” in act can continue folded into every communication. which means, ultimately, that every communication can double into every other communication. (a normal canonical arrange for protein chains, which double into different shapes, is the helix.)imagethe everything font.credit…erik demaine and martin demaine

so, had this clause been written in everything font — with each communication carriage a corrugate design (folding instructions) for another communication — there would continue another clause encoded herein.

** Source: hiTech News Agancy**

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