Related papers: Analyzing the Structure of Mondrian's 1920-1940 Co…
The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference $d(n)$ between the largest and the smallest areas of the rectangles partitioning…
A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic…
It has been claimed [1-6] that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery…
This research extends a method previously applied to music and philosophy,representing the evolution of art as a time-series where relations like dialectics are measured quantitatively. For that, a corpus of paintings of 12 well-known…
Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
How does the machine classify styles in art? And how does it relate to art historians' methods for analyzing style? Several studies have shown the ability of the machine to learn and predict style categories, such as Renaissance, Baroque,…
We report the degree of order of twenty-two Jackson Pollock's paintings using \emph{Hausdorff-Besicovitch fractal dimension}. Through the maximum value of each multi-fractal spectrum, the artworks are classify by the year in which they were…
A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every $k$-colored necklace can be fairly split by at most $k$…
To say that beauty is in the eye of the beholder means that beauty is largely subjective so varies from person to person. While the subjectivity view is commonly held, there is also an objectivity view that seeks to measure beauty or…
In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into $k$ non-congruent rectangles of equal area? This problem is motivated by the so-called `Mondrian art problem' that asks a similar question…
Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order, characterised by long-range translational order. The discovery of…
Quantitative analysis of visual arts has recently expanded to encompass a more extensive array of artworks due to the availability of large-scale digitized art collections. Consistent with formal analyses by art historians, many of these…
The artistic community is increasingly relying on automatic computational analysis for authentication and classification of artistic paintings. In this paper, we identify hidden patterns and relationships present in artistic paintings by…
The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Let $P$ be a set of $n$ points in the plane, not all on a line, each colored \emph{red} or \emph{blue}. The classical Motzkin--Rabin theorem guarantees the existence of a \emph{monochromatic} line. Motivated by the seminal work of Green and…
Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules…
The Art of Memory started with Aristotle's questions on memory. During its long evolution, it had important contributions from alchemist, was transformed by Ramon Llull and apparently ended with Giordano Bruno, who was considered the best…
Painting embodies a unique form of visual storytelling, where the creation process is as significant as the final artwork. Although recent advances in generative models have enabled visually compelling painting synthesis, most existing…