Algorithms of Art Gifts

Negentropy Triptych is an unexpected outcome of a mathematics research project, titled ‘Stress-testing algorithms: generating new test instances to elicit insights’, funded by the Australian Research Council. Professor Kate Smith-Miles’ quest to generate mathematical functions that are challenging and ‘stress-test’ optimisation algorithms has led to a large collection of intricate and beautiful 2D images: contour plots of mathematical functions that have been mathematically generated to create challenging landscapes.

Unable to choose the most beautiful image to print as a poster, she and her co-author, Mario Andrés Muñoz-Acosta, decided to arrange many images into a montage. But what was the most aesthetic arrangement? They noticed the presence of background structure formed as localised connections between the images — meandering ‘blue rivers’ of various lengths — depending on the arrangement.

Surveying friends about their aesthetic preferences — and whether they wanted to see the images rearranged to either enhance or destroy any accidental ‘blue river connectivity’ created by random arrangement — revealed a divergence of taste, and interesting relationships between personality traits and aesthetic preferences for global structure or randomness. Representing this spectrum of preferences as a triptych of images, from disorder to order, thus depicts the emergence of global structure from randomness, and hence the negative of entropy known as ‘negentropy’.

Kate Smith-Miles is a Melbourne Laureate Professor of Applied Mathematics at the University of Melbourne. She was awarded a five-year Laureate Fellowship from the Australian Research Council, and has published two books and over 280 papers on diverse topics in applied mathematics.

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