January 26, 2018 — Christopher Carlson, Senior User Interface Developer, User Interfaces
Every summer, 200-some artists, mathematicians and technologists gather at the Bridges conference to celebrate connections between mathematics and the arts. It’s five exuberant days of sharing, exploring, puzzling, building, playing and discussing diverse artistic domains, from poetry to sculpture.
The Wolfram Language is essential to many Bridges attendees’ work. It’s used to explore ideas, puzzle out technical details, design prototypes and produce output that controls production machines. It’s applied to sculpture, graphics, origami, painting, weaving, quilting—even baking.
In the many years I’ve attended the Bridges conferences, I’ve enjoyed hearing about these diverse applications of the Wolfram Language in the arts. Here is a selection of Bridges artists’ work.
July 19, 2017 — Stephen Wolfram
The Philosophy of Chemicals
“We’ve just got to decide: is a chemical like a city or like a number?” I spent my day yesterday—as I have for much of the past 30 years—designing new features of the Wolfram Language. And yesterday afternoon one of my meetings was a fast-paced discussion about how to extend the chemistry capabilities of the language.
At some level the problem we were discussing was quintessentially practical. But as so often turns out to be the case for things we do, it ultimately involves some deep intellectual issues. And to actually get the right answer—and to successfully design language features that will stand the test of time—we needed to plumb those depths, and talk about things that usually wouldn’t be considered outside of some kind of philosophy seminar.
November 23, 2016 — John Moore, Marketing and Technical Content Team Lead
Over the past few months, Wolfram Community members have been exploring ways of visualizing the known universe of Wikipedia knowledge. From Bob Dylan’s networks to the persistence of “philosophy” as a category, Wolfram Community has been asking: “What does knowledge actually look like in the digital age?”
November 14, 2016 — Kathryn Cramer, Technical Communications and Strategy Group
Today is the 300th anniversary of the death of Gottfried Leibniz, a man whose work has had a deep influence on what we do here at Wolfram Research. He was born July 1, 1646, in Leipzig, and died November 14, 1716, in Hanover, which was, at the time, part of the Holy Roman Empire. I associate his name most strongly with my time learning calculus, which he invented in parallel with Isaac Newton. But Leibniz was a polymath, and his ideas and influence were much broader than that. He invented binary numbers, the integral sign and an early form of mechanical calculator.
October 5, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
After 36 hours, two math graduate students created Draw Anything, the grand prize–winning, Wolfram Cloud–powered app, at the MHacks V hackathon. We’ve written about Olivia Walch and Matt Jacobs’s winning iOS app before. Now, the pair of prize-winning Wolfram hackers have taken the time to talk with us about how they used the Wolfram Language and fast Fourier transforms to create step-by-step drawing guides for any input image—whether it’s a picture of Homer Simpson, a dog, yourself or your future dream car.
May 6, 2016 — Silvia Hao, Consultant, Technical Communications and Strategy Group
Stippling is a kind of drawing style using only points to mimic lines, edges, and grayscale. The entire drawing consists only of dots on a white background. The density of the points gives the impression of grayscale shading.
Back in 1510, stippling was first invented as an engraving technique, and then became popular in many fields because it requires just one color of ink.
Here is a photo of a fine example taken from an exhibition of lithography and copperplate art (the Centenary of European Engraving Exhibition held at the Hubei Museum of Art in March 2015; in case you’re curious, here is the museum’s official page in English).
March 2, 2016 — Michael Trott, Chief Scientist
An investigation of the golden ratio’s appearance in the position of human faces in paintings and photographs.
There is a vast amount of literature on the appearance of the golden ratio in nature, in physiology and psychology, and in human artifacts (see this page on the golden ratio; these articles on the golden ratio in art, in nature, and in the human body; and this paper on the structure of the creative process in science and art). In the past thirty years, there has been increasing skepticism about the prevalence of the golden ratio in these domains. Earlier studies have been revisited or redone. See, for example, Foutakis, Markowsky on Greek temples, Foster et al., Holland, Benjafield, and Svobodova et al. for human physiology.
In my last blog, I analyzed the aspect ratios of more than one million old and new paintings. Based on psychological experiments from the second half of the nineteenth century, especially by Fechner in the 1870s, one would expect many paintings to have a height-to-width ratio equal to the golden ratio or its inverse. But the large sets of paintings analyzed did not confirm such a conjecture.
While we did not find the expected prevalence of the golden ratio in external measurements of paintings, maybe looking “inside” will show signs of the golden ratio (or its inverse)?
In today’s blog, we will analyze collections of paintings, photographs, and magazine covers that feature human faces. We will also analyze where human faces appear in a few selected movies.
November 18, 2015 — Michael Trott, Chief Scientist
Paintings of the great masters are among the most beautiful human artifacts ever produced. They are treasured and admired, carefully preserved, sold for hundreds of millions of dollars, and, perhaps not coincidentally, are the prime target of art thieves. Their composition, colors, details, and themes can fascinate us for hours. But what about their outer shape—the ratio of a painting’s height to its width?
In 1876, the German scientist Gustav Theodor Fechner studied human responses to rectangular shapes, concluding that rectangles with an aspect ratio equal to the golden ratio are most pleasing to the human eye. To validate his experimental observations, Fechner also analyzed the aspect ratios of more than ten thousand paintings.
We can find out more about Fechner with the following piece of code:
May 9, 2014 — Dan Fortunato
If you’ve been anywhere on the internet these past few weeks, there’s little doubt that you’ve come across the game 2048 (made by Gabriele Cirulli). Based on the similar games 1024! (by Veewo Studio) and THREES (by Asher Vollmer), this game has a simple mechanic that can leave you puzzled for days—slide powers of two around a grid, and combine them to make higher powers of two. The goal is to get to 2048. It’s hard to explain just how fun and challenging this game is, so I recommend playing it for yourself.
So, as a tribute to this little game (and in honor of all games mathematical!), I thought it would be fun to demonstrate the power of the Wolfram Language by using it to make our own version of 2048. Let’s go!
The basic structure for the game board will be a 4X4 matrix, initialized with an empty element in each position:
February 12, 2014 — Vitaliy Kaurov, Academic Director, Wolfram Science and Innovation Initiatives
An original gift can make people feel much warmer, especially in the icy weather affecting so many places this winter—including our headquarters. Valentine’s Day is a good excuse to get a little creative in the art of gift making. And for me, “getting creative” long ago became synonymous with programing in the Wolfram Language. It is that medium that compels me to treat programming as art, where one can improvise, easily pulling magical rabbits out of a hat.
So what shall we make? I think the best gift is a DIY one—especially if it says a lot without even making a sound. Below you see a 3D-printed silver earring in the shape of a sound wave recorded while a person is saying “I love you.”