Letter I

IM

The submitted artwork visually represents the interplay between mathematical patterns and perceptual anomalies, embodying the essence of anomalous mathematical patterns. Through the use of parallel and intersecting lines, the piece evokes principles from linear algebra and geometry, particularly in the study of vector spaces and transformations. The structured yet chaotic arrangement suggests the presence of fractal-like self-similarity, where small segments echo the overall composition, a key concept in dynamical systems.

Additionally, the shifting color gradients and distortions evoke wave interference patterns, reminiscent of Fourier transforms and spectral decomposition. The juxtaposition of rigid, straight lines with seemingly fluid distortions creates a visual paradox, akin to paradoxical mathematics, where established rules produce unexpected outcomes. This interplay aligns with the mathematical study of moiré patterns, which emerge when periodic structures overlay and interfere, producing emergent behaviors not present in the individual components.

Furthermore, the composition engages with the notion of visual entropy—balancing order and disorder—mirroring mathematical explorations of chaos theory. By embracing both predictability and unpredictability, this piece illustrates the tension between structure and randomness, a fundamental aspect of mathematical modeling in complex systems. In doing so, the artwork becomes a bridge between abstract mathematical principles and human perception, encapsulating the theme of the contest.

Lasha Inashvili

Title: A fly in a mathematician’s room

The work is based on my understanding and intuition (I am not a mathematician or a physicist), which I developed while reading some popular sources about the subject, including those recommended by the institute.

A fly flies into the room and, having enough space, makes random movements in the air (of course, in real life, they might not be absolutely random and might depend on other factors/conditions). Once the fly enters the space confined by the aquarium walls and hovers above the water, it faces physical barriers—the aquarium walls. To the best of my understanding, the fly’s movements/trajectories above the aquarium water resemble anomalous diffusion.

The graphics (“artistic” drawing) were done on a tablet with a canvas resolution of 4000 x 3200 pixels and resemble a chalk drawing on a blackboard. I selected this style because, in my opinion, it resonates with the subject of mathematics in general.

The main idea was to illustrate the subject in a relatively simple and, at the same time, engaging way. I am not sure if I succeeded or made no mistakes in demonstrating the subject in this particular way, but at least I tried my best.

Indrė

Given a bit thought, this quite complex theme became more simple. Not only maths and science, but nature has such patterns as well. Animals do not walk on the same path while searching for a new living place. A bit harsh representation, but squares in this painting show different habitats, nature settings. These foxes are looking for a place to live, which isn’t already taken. A bit of an Easter egg, but there are birds prints on the square they are looking at, which indicates that the food for surviving won’t be a problem if they decide to stay.

Freya Irvine

There is structure here, through all of its squares and right angles, however, just like life, not every piece is in the “correct” or straight position and yet they all fit together perfectly, like it was designed. 

Andrew Irving & Ebrahim Patel

Video https://drive.google.com/file/d/1XlPSQYBJb5Ppo01EPZseByWZY87ysRrE/view?usp=sharing

You are about to watch a Stop-Motion movie, inspired by Anomalous Diffusion.

Anomalous diffusion takes place when particles diffuse across `fractal' structures, the kind that branch like the networks of nerves that fill our bodies.

In our movie, each one of 700+ frames tracks 1 million points that reveal a fractal structure.  Each fractal is regarded as an `Attractor', as it `attracts' the points of what mathematicians call a dynamical system (DS).

A DS uses some rule(s) to determine where some point(s) should be on the computer screen.  Colloquially, the type of DS we have used is known as a `Chaos game' (though more formally, we call it an `Iterated Function System').

Any 2 consecutive frames of this movie feature attractors from two similar, but not identical, dynamical systems.  These attractors are therefore similar, but not identical, in appearance.  We perturb the settings (DS parameters) that create one, to create the other.

Thus, we demonstrate the relationship between different dynamical systems via their attractors - by imagining the transitions from one attractor to another.

Visually, it is as though 1 million `particles' are moving on a continuously-evolving fractal structure.