Math illustrations series#
And the illustrations in his “ Calculation” series are incredibly detailed and gorgeous - they’ve even been compared to Da Vinci’s sketches. His fascination with these patterns has led to a 40 year career of drawing super precise 3D illustrations that he creates by hand, without any assistance from computers. “In a similar way a geologist sees patterns in rocks, I see them in nature as a whole,” Araujo tells Inverse. He can instantly spot what he describes as intelligent patterns - spirals and gentle curves in rocks, flower petals, leaves, shells, insect formations, and other objects in nature. The National Science Foundation, Defense Advanced Research Projects Agency, the Sloan Foundation, Microsoft Research and the Packard Foundation supported this research.When artist and architect Rafael Araujo needs inspiration to create a new illustration, all he has to do is look out the window of his studio in Caracas, Venezuela. Keenan Crane, July 2020, ACM SIGGRAPH International Conference on Computer Graphics and Interactive Techniques. Reference: “Penrose: from mathematical notation to beautiful diagrams” by Katherine Ye, Wode Ni, Max Krieger, Dor Ma’ayan, Jenna Wise, Jonathan Aldrich, Joshua Sunshine and “Our vision is to be able to dust off an old math textbook from the library, drop it into the computer and get a beautifully illustrated book - that way more people understand,” Crane said, noting that Penrose is a first step toward this goal.
Math illustrations software#
In addition to Ye and Crane, the team included Nimo Ni and Jenna Wise, both Ph.D students in CMU’s Institute for Software Research (ISR) Jonathan Aldrich, a professor in ISR Joshua Sunshine, an ISR senior research fellow cognitive science undergraduate Max Krieger and Dor Ma’ayan, a former master’s student at the Technion-Israel Institute of Technology.
“We let them define whatever notation they want, so they can express themselves naturally.”Īn interdisciplinary team developed Penrose. “Mathematicians can get very picky about notation,” he explained. The research team developed a special programming language for this purpose that mathematicians should have no trouble learning, Crane said. The user can then select and edit the diagrams they want from a gallery of possibilities. Once the computer learns how the user wants to see mathematical objects visualized - a vector represented by a little arrow, for instance, or a point represented as a dot - it uses these rules to draw several candidate diagrams. “The secret sauce of our system is to empower people to easily ‘explain’ this translation process to the computer, so the computer can do all the hard work of actually making the picture.” student in the Computer Science Department. “We started off by asking: ‘How do people translate mathematical ideas into pictures in their head?'” said Katherine Ye, a Ph.D. The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held virtually this July because of the COVID-19 pandemic.Ī new software tool from Carnegie Mellon University turns abstract mathematical expressions into pictures than can be more easily understood. Other users can then access this capability using familiar mathematical language, leaving the computer to do most of the grunt work.
Penrose addresses these challenges by enabling diagram-drawing experts to encode how they would do it in the system. “We want to make this expressive power available to anyone.”ĭiagrams are often underused in technical communication, since producing high-quality, digital illustrations is beyond the skill of many researchers and requires a lot of tedious work. “Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased,” said Keenan Crane, an assistant professor of computer science and robotics. The researchers named it Penrose after the noted mathematician and physicist Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical and scientific ideas.
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