Optimal construction of montages from mathematical functions on a spectrum of order–disorder preference

ABSTRACT We previously generated diverse mathematical functions that are difficult for optimization algorithms. Represented as 2D contour plots, each image depicts a ‘blue river’ running through an intricate landscape. This paper describes the challenge of constructing an aesthetic montage of these images. A survey revealed a spectrum of tastes, divergent in preference from order to disorder, considering the structure created by connecting these ‘blue rivers’. A new artwork, Negentropy Triptych, was created to depict this spectrum by manually swapping images from a random arrangement, guided by human eye to enhance or destroy the structure. An optimization algorithm automates the process, with the results of its efforts to emulate the artistic vision presented and discussed. The challenges faced by the algorithm, despite exploring several objective functions, highlight the difficulties of capturing the goals that a human decision-maker can easily achieve. Therefore, machine learning of these goals is a promising future direction. GRAPHICAL ABSTRACT