Letter C

Sofia Candeo (Art Syamhope)

Video https://drive.google.com/file/d/1PGeJhX1S1ot3EJTj5psil51KPm07eiJY/view?usp=sharing

Emma-Louise Cartwright

The title of this artwork, A Terrible Beauty, is a fragment of a line from W.B. Yates’ poem, Easter, 1916 (Poetry Foundation, 2019). Its context is changed here to describe hurricanes as a force of awe and terror—their unpredictability possibly addressed by ‘stochastic analysis’ (Katz, 2002). In keeping with the competition’s remit, this elemental piece seeks to convey to a broad audience the beauty of mathematics through art and its value in solving real-world issues.

Scientists and meteorologists have long struggled to predict storms, especially in regions more vulnerable to hazardous weather (Basineni, 2024), which may continue to develop due to climate change. Stochastic systems are one method of tackling this problem, as they can model the anomalous diffusion found in hurricanes.

The word ‘stochastic’ (2025) comes from the Greek term stokhastikos, meaning ‘skilful in aiming’ or ‘able to guess’. Weather forecasting can use stochastic systems—a family of mathematical models which include uncertainty and randomness when describing a physical process—to better predict the trajectory of hurricanes. This, in turn, could result in improved reliability and accuracy of forecasts (Pathak et al., 2018), meaning lives could be saved.

A separate reference list can be provided on request for these in-text citations.

Christian Casaljay

Title: The Microcosm of Milk

This artwork delves into the microscopic events within organic milk, capturing the vibrant activity of living organisms that sustain its nutritional essence. Beyond its biological significance, the piece reveals a tapestry of anomalous mathematical patterns inherent in nature. The intricate lattice-like structures, swirling formations, and spherical clusters echo fractal geometry and fluid dynamics. These patterns, often unnoticed in our daily consumption, represent the invisible harmony between biology and mathematics. The artwork challenges traditional perceptions, showing how life’s smallest components resonate with universal mathematical principles.

Aishik Chakma (Entry 1)

Title:" Hidden Signals in Chaos"

This artwork shows relationship between randomness and structure in stochastic processes, in which hidden signals are commonly masked by noise. The variations of the swirling, chaotic textures depict erratic fluctuations; the still emerging patterns reflect an underlying order awaiting discovery.” This interplay aligns with how mathematics factors into the real world, from financial systems to natural phenomena to well mathematical models, where it’s important to know what’s signal and what’s noise.                                    

Mathematically, it is accrued from the field of signal processing or probability theory; we use filtering techniques to acquire patterns from noisy data. The color shifts and liquefied movement play into how signals are born and die inside stochastic environments that are constantly at odds with clarity of signal and distortion. An algorithmic procession that is both organized and chaotic, the arrangement invites viewers to think about how randomness can both obscure and expose hidden realities.

Aishik Chakma (Entry 2)

This captivating artwork brings to life the mathematics of diffusion, a process governed by stochastic movements and random walks. Waves of fiery oranges, deep blues, and rich purples ripple across the canvas, tracing the erratic journey of particles through space. The turbulent yet balanced flow mirrors diffusion’s impact across physics, biology, and machine learning—shaping polymer formations, microbe trajectories, and statistical algorithms.

Exploring anomalous diffusion, the piece captures deviations from classical models. Dark, dense patches suggest confinement, while vibrant, expansive streaks hint at acceleration, reflecting effects like boundary reflections or adaptive dynamics. The swirling forms evoke feedback loops and spatial anisotropy—where processes interact with their past or environment, as seen in foraging animals avoiding retraced paths or efficient sampling algorithms navigating space. Each curve reveals the tension between structure and chaos, from resource-driven motion to excluded volume effects in polymers.

This artwork transforms abstract stochastic concepts into an immersive, thought-provoking experience. It invites viewers to feel the restless beauty of anomalous diffusion, where probability and innovation converge in a striking visual display that bridges mathematics and creativity.

Aishik Chakma (Entry 3)

This artwork shows the concepts of Power Laws, where small dominant elements govern the effect of the much greater volume of other elements in the system. There is a grid with blocks of different sizes, which reflects the hierarchy of power-law distributions. Stronger, larger areas — larger in terms of both color saturation and structural complexity — represent a few strong elements that dominate the entire system. The smaller blocks that sat at the bottom of the vector were the less notable events or entities that form a long tail that together represent the most but on an individual basis isn't terribly important.

Power laws are that govern characteristics of things in nature, economics, and networks—for instance, wealth distribution, earthquake magnitudes, and internet connectivity—where a couple of big things outweigh a significant number of smaller things. The spiral-type central focus corroborates with logarithmic spirals, bands often found in systems driven by power laws, such as galaxies and population distributions. This transition from ordered to chaotic regions exemplifies the unpredictable, but structured behavior that such distributions exhibit.

This work connects abstraction with mathematical principles, inviting viewers to consider ways hidden structures affect the world around us.

Romane Charpentier

This illustration highlights the diversity of mathematics and its connections to our environment, including through anomalous phenomena. The childlike style of the image is a deliberate choice to attract the attention of a wide audience.

Mathematics is intrinsically present in nature, as seen in the geometric shapes of shells, sunflowers, ferns, and the hexagons of honeycombs in beehives. Nature is also a source of inspiration for mathematicians to develop models such as predator-prey dynamics, river flow and resource management. Even randomness, as observed in population dynamics, has its own mathematical theory. 

The behaviour of our own bodies, how sport modifies us, how diseases spread, and even how, in the brain, the degree of depolarisation of a neuron predicts its firing rate, all follow mathematical models—though many are not yet fully understood.

Human innovations in telecommunications, architecture, transportation, and renewable energy production heavily rely on mathematical concepts. Mathematics not only allows us to observe the invisible, whether through an astronomical telescope or an electron microscope, but also helps us to predict the unknown via machine learning.

The richness of mathematics and the way it intertwines with our environment, even in its most fundamental aspects, are reflected in this illustration.

Bineet Singh Chawla

Betting is often seen as a game of chance, but in reality, it is a game of probability and statistical certainty—where the house always wins. This artwork visualizes the hidden mathematical forces that govern online betting platforms like Stake. Instead of luck or intuition, the system operates on probability distributions, Monte Carlo simulations, and expected value calculations, ensuring that the platform remains profitable no matter how bets are placed.

The image removes human emotion from the equation, focusing purely on the mathematical machinery behind betting. Floating probability curves, shifting odds, and algorithmic adjustments dictate outcomes while golden currency continuously flows into Stake’s vault. The translucent, digital hand symbolizes the unseen forces controlling the betting landscape—where every number is optimized for profit.

The cyberpunk aesthetic enhances this process's futuristic, almost surreal nature—where bettors believe they have a chance, yet the mathematical reality is already written. This piece challenges viewers to question the illusion of control in gambling and recognize that probability is not just a number—it is the silent architect of profit.

Mwewa Annie Chipepo 

This image beautifully captures the essence of anomalous diffusion in stochastic systems, presenting a cosmic dance of particles traversing an unpredictable landscape. The intricate swirls of light and energy symbolize the varying trajectories governed by stochastic processes. Some particles move steadily, representing subdiffusion, while others take brilliant, sudden leaps, showcasing superdiffusion. 

The radiant colors—fiery golds, deep purples, and ethereal whites—evoke the interplay between order and chaos, embodying the complexity of fractional Fokker-Planck equations. The nebulous background represents the medium’s constraints, highlighting how randomness is shaped by underlying physical or biological processes. This artwork of mine transcends its visual appeal, serving as a bridge between science and art, making the abstract concepts of stochastic systems and anomalous diffusion tangible and awe-inspiring.

Ming Yi Chung (Entry 1)

It presents a fractal pattern. Fractals are an important concept in abnormal mathematics and have self - similarity, that is, they exhibit similar shapes at different scales. The pattern progresses from the center to the outer layers, and the details of each layer are similar to the whole, embodying the infinite details and self - similarity characteristics of fractals, and demonstrating the complexity and beauty of mathematical structures.

Ming Yi Chung (Entry 2)

The shape is like a radial geometric structure, involving concepts of symmetry and spatial topology. The spikes radiating evenly from the center reflect rotational symmetry, which is studied in group theory and geometry in mathematics, and reflects the exploration of spatial forms and symmetry laws in mathematics.

Ming Yi Chung (Entry 3)

It is a reticular three - dimensional structure, involving concepts of topology and geometry. The holes and connecting lines form a specific spatial configuration, similar to the study of spatial connectivity and shape in topology, demonstrating the role of mathematics in describing and understanding spatial forms.

Piotr Cieślak

My submission is a solarigraphic photograph that captures the interplay of time, light, and randomness, aligning with the themes of anomalous mathematical patterns. Solarigraphy is a photographic technique utilizing pinhole cameras for extended exposures, often spanning weeks or months. This method creates unique images that document the sun’s path across the sky and the surrounding environment, revealing hidden patterns shaped by both natural and stochastic processes.

In this work, the seemingly deterministic motion of the sun interacts with unpredictable factors such as weather changes, atmospheric conditions, and the imperfections of the handmade pinhole camera. These variables introduce an element of randomness that becomes integral to the final image. The resulting photograph is a visual representation of both order and chaos, showcasing how structured paths can intertwine with anomalies to create something both scientifically intriguing and aesthetically captivating.

Through this approach, I aim to explore the inherent unpredictability of natural systems and the beauty that emerges from it. Solarigraphy serves as a bridge between art and science, illustrating complex patterns and highlighting the relationship between mathematical abstraction and the organic randomness of the physical world. This work invites viewers to reflect on the hidden structures and anomalies that govern our universe.

Jacek Cislo (Entry 1)

Water splash is an example of nonlinear fluid dynamics and can be described mathematically using the Navier-Stokes equations, which model the motion of a liquid by taking into account internal and external forces:

ρ(∂v∂t+(v⋅∇)v)=−∇p+μ∇2v+f

ρ(∂t∂v​+(v⋅∇)v)=−∇p+μ∇2v+f

where:

ρρ – fluid density,

vv – velocity,

pp – pressure,

μμ – viscosity,

ff – external forces (e.g. gravity).

During splashing, surface forces and surface tension are key, which affect the shape and direction of the splash. A high Reynolds number (Re≫2000Re≫2000) means that the flow is turbulent, which causes chaotic spray.

In simple terms, water hits the surface, the forces acting on it cause the droplets to spread in different directions according to the equations above.

Jacek Cislo (Entry 2)

The process of reflection of an object in a water surface can be explained using symmetry with respect to a plane and the laws of light reflection.

Mathematically, reflection can be described as axial symmetry with respect to the water surface. If the water surface is at a height of y=0y=0, then the object point with coordinates (x,y)(x,y) after reflection will have coordinates (x,−y)(x,−y).

Additionally, light is reflected according to the law of reflection:

angle of incidence=angle of reflection

angle of incidence=angle of reflection

which means that if a light ray falls at an angle θθ to the surface, it will reflect at the same angle.

Thanks to these two principles, the human eye interprets the reflection as a symmetrical image with respect to the water surface. If the surface is wavy, the reflection becomes distorted, which results from local changes in the angles of reflection.

Jacek Cislo (Entry 3)

An example of a photo that addresses the issue of kinetics: In a mathematical context, analyzing standing up from a chair, one can study changes in the angles of the hip, knee and ankle joints over time, angular velocities and moments of force acting in individual joints. Such analyses allow for a detailed understanding of the biomechanics of movement and are used in scientific research and clinical practice to assess the motor functions of patients.

In a mathematical context, kinetics describes these movements using equations that take into account forces, moments of force, and angular and linear accelerations of individual body segments. For example, the moment of force (MM) acting on a joint can be calculated as the product of the force (FF) and the arm of the force (rr):

M=F×rM=F×r

Where:

FF – muscle force,

rr – distance from the axis of rotation (joint) to the point of application of the force.

By analyzing these relationships, you can understand what forces and moments are needed to perform the movement of getting up from a chair and which muscles are responsible for it.

Ken Clarry

Link https://drive.google.com/file/d/1qEHED5mXG52oRluXCVPGvaGmuJG8EMBV/view?usp=sharing

This art project compares the current state of the world to Chaos Theory, where actions or events disperse globally, emulsify and emerge as secondary interactive phenomena. Most often we experience these events in current affairs programmes and news reporting on television and the Internet. A socio-environmental example of an event is the Industrial Revolution and its dependence on fossil fuel. This ‘material advancement’ contributes to climate change and global warming.  Each event has a complex thread of historical action linked to SDIC (Sensitive Dependence on Initial Conditions).  In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state can result in large differences in later states.  My art practice uses the concept of ‘butterfly effect’ to produce diffused progressions: thought elements, patterns, actions that move through space, time and machine, influenced by random effects.  It begins as reaction to reporting of catastrophic events and media photographs sourced from the Internet, a time-line of displaced iterations.  The found image is subjected to a set of computer commands over which outcomes I have no control.  I select final art images as aesthetic decisions: do they work to aesthetic principles/patterns, and do they move sensorially? 

Conor Collins

This portrait of Alan Turing is composed of binary code, forming a hidden message within the image. Binary—1s and 0s—represents the fundamental language of modern computing, but here, it also embodies a deeper concept of pattern, disruption, and transformation. 

Turing, a mathematician whose work on cryptography and computation changed the world, was also a victim of systemic discrimination. The portrait is rendered in the colours of the Trans Pride Flag, acknowledging historical cycles of marginalisation. Mathematical systems describe disorder within structured frameworks—here, identity itself becomes the variable within a rigid social equation.

If the binary code is translated, it reveals a quote attributed to Turing: "Sometimes it is the people no one can imagine anything of who do the things no one can imagine." Just as stochastic processes allow for unexpected outcomes, so too do human lives defy imposed limitations. In both mathematics and society, outliers are not errors; they are the catalysts for progress.

Kathryn Cooper

Video https://drive.google.com/file/d/14VRMHLcQqx6iaaTYwa1n3kJc97LusRPP/view?usp=sharing

In a flock of starlings, nature has evolved a system that is robust to predation; where many eyes look out for attack, and where risk is shared amongst the group. Remarkably, the group achieves this without any leadership structure, the simple local interactions between individuals creating outcomes greater than the sum of their parts.

The birds neither collide nor disperse, effortlessly avoiding obstacles and evading predators. As they pass overhead, they fill the air with an astonishing barrage of noise and vibration of the air. Not only are they visually breathtaking, but they engulf the other senses.

The way that starlings behave in a group is a beautiful example of a complex system, in that there are many interacting parts. Interesting and unexpected global behaviours emerge from these interconnected environments.

What makes flocks particularly fascinating is that the interaction network (how we describe which starling interacts with which) dynamically changes as the birds move relative to each other.

Murmurations are a compelling visual metaphor from nature and a point of accessibility to the complicated mathematics that is increasingly impacting all our lives.

Rashid Cornish

These paintings are geometric abstractions inspired by stochastic systems and anomalous diffusion, depicting a dynamic interplay of order and randomness. A dense network of interwoven polygons—primarily rectangles, triangles, and irregular quadrilaterals—forms the foundation, with sharp edges and layered transparency suggesting a complex, non-linear evolution. The warn and cool color palettes combined with strong contrast in value represent areas of high and low diffusion activity. Gradients and fading edges mimic probability distributions, where particles exhibit erratic motion.

Throughout the compositions, certain regions appear frozen in structured lattices, while others dissolve into chaotic fragmented clusters. Curvilinear pathways of minute stippled dots trace the unpredictable trajectories of diffusing elements, sometimes aggregating into dense edges, sometimes dispersing into deep voids.

The contrast between rigid geometry and fluidity echoes the paradox of constrained randomness found in stochastic processes. The layering of semi-transparent forms creates depth, reinforcing the impression of a constantly shifting, emergent order. These paintings capture the beauty of unpredictability—where chaos and structure converge in a mathematically inspired dance of motion and stillness.