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.
February 26, 2016 — Emily Suess, Technical Writer, Technical Communications and Strategy Group
Kip Thorne, physicist, New York Times bestselling author, and professor emeritus at Caltech, ignited fans’ passion for science through his work on the movie Interstellar. The sci-fi adventure won the 2015 Academy Award for Best Visual Effects, and the first cuts of some of those stunning visuals were created with Mathematica and the Wolfram Language.
“Mathematica was my way of testing whether or not I had the equations right,” says Thorne, whose computational approach to producing images led to publication in the American Journal of Physics and Classical and Quantum Gravity.
February 3, 2016 — Bernat Espigulé-Pons, Consultant, Technical Communications and Strategy Group
When I hear about something like January’s United States blizzard, I remember the day I was hit by the discovery of an infinitely large family of Koch-like snowflakes.
The Koch snowflake (shown below) is a popular mathematical curve and one of the earliest fractal curves to have been described. It’s easy to understand because you can construct it by starting with a regular hexagon, removing the inner third of each side, building an equilateral triangle at the location where the side was removed, and then repeating the process indefinitely:
If you isolate the hexagon’s lower side in the process above you’ll get the Koch curve, described in a 1904 paper by Helge von Koch (1870–1924). It has a long history that goes back way before the age of computer graphics. See, for example, this handmade drawing by the French mathematician Paul Lévy (1886–1971):
December 4, 2015 — Bernat Espigulé-Pons, Consultant, Technical Communications and Strategy Group
About a year ago, I decided to record every single move I make using Runkeeper, and now I want to make some visualizations of my activity throughout the whole year. This is a fairly straightforward project where I will download the data from Runkeeper, then use the Wolfram Language to process, analyze, and visualize my activities. I will show how to create animations like this one that superimposes 24 minutes of all my activities recorded in Barcelona:
October 14, 2015 — Wolfram Blog Team
The first Democratic debate of the 2016 election season has finally come to pass. Although the Democratic party has less than half the number of candidates as the Republican party, this event was just as lively and saw just as much hype. As we did for the two GOP debates, we used last night’s transcripts of everything the candidates said to create linguistic images using the WordCloud function.
In case you missed our previous posts, WordCloud is a Wolfram Language function that allows anyone to visualize words, sized by their frequency in a text. With just one line of code, you can create a word cloud graphic from data, text, or URLs.
September 18, 2015 — Jonathan Wallace, Manager, Marketing Communications
After the first Republican presidential debate, we showed you how the WordCloud function in the Wolfram Language can be used to create compelling visualizations of what the candidates said.
This time around, Alan Joyce and Vitaliy Kaurov have done an even cooler analysis over at Wolfram Community, delving further into what words were used most frequently and what subjects the candidates had in common—and how they set themselves apart.
For example, check out the words uniquely used by each candidate in Wednesday’s debate below.
August 13, 2015 — Jonathan Wallace, Manager, Marketing Communications
A few days ago, Fox News hosted the first presidential primary debate of 2016. The candidates met onstage, vying for support from the GOP electorate. Among the cacophony and crafty messaging, a truly artful winner has emerged: word clouds.
The WordCloud function (1 of 5000+ functions) in the Wolfram Language allows anyone to visualize words, sized by their frequency in a text. With a mere line of code, you can create a compelling word cloud graphic from data, text, or URLs.
But don’t take my word for it; let’s make the WordCloud function earn your support.
July 2, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group
We’re always on the lookout for new ideas and ways of using the Wolfram Language that our users produce and choose to write about in their books. In this quarter, we have applications that bridge the gap between art and geometry, and demonstrate intuitive data analysis. In addition to writing books, Wolfram welcomes authors to submit articles for publication in The Mathematica Journal, our very own in-house periodical.
April 21, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group
What do genealogy, linear algebra, and the Raspberry Pi have in common? Not much, but they come together in this diverse and engaging assortment of books by the international community of authors employing Wolfram technologies in their work.
April 14, 2015 — Alan Joyce, Director, Content Development
Wolfram|Alpha’s Facebook analytics ranks high among our all-time most popular features. By now, millions of people have used Wolfram|Alpha to analyze their own activity and generate detailed analyses of their Facebook friend networks. A few years ago, we took data generously contributed by thousands of “data donors” and used the Wolfram Language’s powerful tools for social network analysis, machine learning, and data visualization to uncover fascinating insights into the demographics and interests of Facebook users.
At the end of this month, however, Facebook will be deprecating the API we relied on to extract much of this information.