One of the most interesting points to me in this week's topics was the slow yet methodical evolution of the interplay between art and mathematics. In Professor Vesna's online lecture, we are taught about how artists such as Brunelleschi first formulated the mathematical foundations of linear perspective in order to more accurate portray reality in their drawings. In other words, these artists saw the mathematical beauty in nature. It is interesting to see how in the present day, we have an increasing number of mathematicians doing the converse - finding the artistic beauty in mathematics. Take the Mandelbrot set, for instance:
The Mandelbrot set refers to a particular solution set of the quadratic recurrence equation. Plotted on a complex plane, the Mandelbrot set produces a mesmerizing, infinitely complex image well-known by both mathematicians and artists all around the world.
As an electrical engineer, my fascination with mathematics is its ability to quantify and explain the world around us in a way that it reveals the "beauty", or "art", that is seemingly hidden in nature. There is a great example of this found in a work of art produced by Nathan Selikoff.
Employing this concept in the context of audio works very well. As we view audio transformed into the frequency domain, we can clearly see high-frequency components become larger when a high-pitched voice is introduced, and low-frequency components become larger as low-pitched sounds are introduced. This is used to great effect in applications such as audio visualizers and shows a way in which we can use mathematics to reveal the artistic beauty in something like sound.
This week's learning materials really demonstrated to me the intimate relation between math and art. The frequency with which artists find mathematical beauty in their work, or with which mathematicians find artistic beauty in their work, lends credibility to the idea that the two are inseparable. I look forward to seeing other ways in which this is expanded upon in this course.
Sources
"Chapter 3: The Frequency Domain." Music and Computers. Columbia University Computer Music Center, n.d. Web. 16 Apr. 2017.
Echo93611. "Unity Music Visualizer V2." YouTube. YouTube, 10 Aug. 2014. Web. 16 Apr. 2017.
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| Zooming in on the Mandelbrot set produces infinitely many different patterns, all a result of mathematics. |
The Mandelbrot set refers to a particular solution set of the quadratic recurrence equation. Plotted on a complex plane, the Mandelbrot set produces a mesmerizing, infinitely complex image well-known by both mathematicians and artists all around the world.
As an electrical engineer, my fascination with mathematics is its ability to quantify and explain the world around us in a way that it reveals the "beauty", or "art", that is seemingly hidden in nature. There is a great example of this found in a work of art produced by Nathan Selikoff.
In this video, Nathan has visualized sound by plotting its frequency components on a circular clock face. This is a great example of the mathematical concept of the frequency domain transformation. The concept behind the "frequency domain" is that any arbitrary signal varying in time or space can be thought of as the sum of sinusoids of different frequencies.
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| An approximation of a square wave in frequency domain. Note that the frequency domain represents the approximate magnitudes of the different frequency sinusoids comprising the square wave. |
Employing this concept in the context of audio works very well. As we view audio transformed into the frequency domain, we can clearly see high-frequency components become larger when a high-pitched voice is introduced, and low-frequency components become larger as low-pitched sounds are introduced. This is used to great effect in applications such as audio visualizers and shows a way in which we can use mathematics to reveal the artistic beauty in something like sound.
This week's learning materials really demonstrated to me the intimate relation between math and art. The frequency with which artists find mathematical beauty in their work, or with which mathematicians find artistic beauty in their work, lends credibility to the idea that the two are inseparable. I look forward to seeing other ways in which this is expanded upon in this course.
Sources
Echo93611. "Unity Music Visualizer V2." YouTube. YouTube, 10 Aug. 2014. Web. 16 Apr. 2017.
Fourier Transform - Time and Frequency Domains. Digital image. Wikipedia. Wikimedia Foundation, n.d. Web. 16 Apr. 2017. <https://upload.wikimedia.org/wikipedia/commons/5/50/Fourier_transform_time_and_frequency_domains.gif>.
Frantz, Marc. Lesson 3: Vanishing Points and Looking at Art. N.p.: University of Central Florida - Department of Computer Science, n.d. PDF.
"Mandelbrot Set." Mandelbrot Set -- from Wolfram MathWorld. Wolfram Research, n.d. Web. 16 Apr. 2017.
Selikoff, Nathan. "Audiograph - Interactive Public Art Installation." Vimeo. N.p., 3 Nov. 2015. Web. 16 Apr. 2017.
Uconlineprogram. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. YouTube, 09 Apr. 2012. Web. 16 Apr. 2017.
Weisstein, Eric W. "Mandelbrot Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MandelbrotSet.html
Frantz, Marc. Lesson 3: Vanishing Points and Looking at Art. N.p.: University of Central Florida - Department of Computer Science, n.d. PDF.
"Mandelbrot Set." Mandelbrot Set -- from Wolfram MathWorld. Wolfram Research, n.d. Web. 16 Apr. 2017.
Selikoff, Nathan. "Audiograph - Interactive Public Art Installation." Vimeo. N.p., 3 Nov. 2015. Web. 16 Apr. 2017.
Uconlineprogram. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. YouTube, 09 Apr. 2012. Web. 16 Apr. 2017.
Weisstein, Eric W. "Mandelbrot Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MandelbrotSet.html
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