Letter H

Henry Hagger

Link https://docs.google.com/document/d/1Au3cMUuAtLsSL8y8tor5dw3TJP-APQG7/edit?usp=sharing&ouid=104249367324869316652&rtpof=true&sd=true

A visual expression of an exercise in probability. Taking 3 primary colours and 3 secondaries, selecting in groups of 4 gives 15 possibilities. Arranging these in 3 rows of 5 such that no colour repeats in the same position within any square in the same row, either vertically or horizontally. The solution shown may be rotated horizontally or vertically and still meet these requirements.  How many other possibilities are there if the position of the four colours in each group is altered ?

Artistically, the image is strengthened with the addition of embossing and debossing which adds texture but not colour.

The matrix from which the prints were taken was hand cut by the artist.The prints, on Hahnemuhle paper, were made by the artist on a Rochat press at Artichoke studios in London during Spring 2025

Alfiq Haikal

Title: Celestial Anomaly: The Stochastic Veil

In the vast expanse of the cosmos, nebulae appear as mere chaotic formations, yet hidden within their beauty lies intricate stochastic patterns governed by complex mathematical principles. This artwork portrays the interaction between anomalous diffusion and fractal structures, where the cosmic flow of matter forms non-linear dynamics seemingly random yet deeply mathematical.

The veiled figure symbolizes the controlled chaos observed in stochastic systems in modern physics. The flowing cosmic material follows dynamics akin to anomalous diffusion, a phenomenon where particles disperse in a way that defies classical Brownian Motion.

Through this piece, viewers are invited to explore how mathematics is not just an analytical tool but also an artistic medium, revealing the hidden order within disorder where the universe continuously weaves mesmerizing patterns in the void.

Zlatoslava Halian

Video https://drive.google.com/file/d/1yWAcYlL7KNTj9Dt59rOC0Wc8OuyU5Rol/view?usp=sharing

My sculpture brings to life the Chen–Gackstatter surface, a minimal surface with one end and an intrinsic curvature that balances complexity and elegance. This form embodies the interplay of regularity and anomaly in mathematical structures, revealing the delicate harmony between symmetry and distortion. 

The sculpture's undulating geometry mirrors diffusive processes and the fluid-like behavior of minimal surfaces, while its intricate folds evoke interacting random walks and the dynamic flow of energy in nature. By translating an abstract mathematical construct into tangible form, the artwork bridges the gap between theoretical beauty and physical presence, inviting viewers to explore the hidden patterns that govern space and form.

This artwork was created in collaboration with mathematicians, whose expertise and insights inspired me to transform an abstract equation into a tangible form. By bridging mathematics and art, I aimed to give physical presence to a structure that previously existed only in theory, making its hidden beauty visible and perceptible to all. 

Christopher Hanusa (Entry 1)

A classic knight’s tour is the movement of a knight around a chessboard in such a way that it visits each of the 64 squares and returns to its starting location. This artwork, entitled Playing 4D Chess, is a visualization of a knight’s tour on a four-dimensional chessboard. The 80 chambers on the 3x3x3x3 chessboard (removing the central chamber) are each represented by a small node; a knight’s move is a displacement of two units in one direction and one unit in an orthogonal direction. The first three dimensions (x,y,z) are shown in a standard 3D grid. A unit move in the fourth dimension is represented by a translation of (1/4,1/4,1/4); vertices for a fixed 3D slice have a consistent form (cube, sphere, or octahedron) to aid in the visualization. The viewer is encouraged to play 4D chess by following the path as it visits each of the 80 vertices and returns to where it started. As they do, they will see that no two consecutive moves involve the same two coordinates. The viewer can notice intriguing patterns involving parallel trajectories and how traveling in the fourth dimension corresponds to shorter or longer paths than they might expect.

Christopher Hanusa (Entry 2)

Platonic Neurons consists of five 3D printed sculptures that straddle the domains of mathematics, computer science, and biology. These polyhedral neurons are created by choosing random points inside the solid, procedurally weighting the distances between them, and using Kruskal's algorithm to find a minimum weight spanning tree that connects all the points. The generative nature of the placement of the nodes leads to an organic result. Just as in a neuron, the center of each sculpture serves as the hub of the network. There is one sculpture for each of the classic platonic solids (Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron). The neurons are individually 3D printed in nylon and carefully hand dyed to create a vibrant radial gradient.

Shamita Harithsa

I would like to briefly elaborate on the concept that inspired this piece. My favorite book during my childhood was A Brief History of Time by Stephen Hawking. The information paradox remains a mystery in the field of mathematics and cosmology. It challenges our understanding of quantum mechanics. Hawking initially explained that when matter falls into a black hole, information about its properties (such as mass and charge) are lost. As the black hole emits thermal radiation, it theoretically evaporates—causing the information to disappear. This conflicts with quantum mechanics, which requires information to be conserved.

My artwork explores this paradox under the theme of stochastic systems and anomalous diffusion—both of these concepts involve unpredictability, irregularities and deviations from classical laws of Physics. The man represents the many physicists and mathematicians fascinated by this bizarre phenomena. In portraiture, the eyes often symbolize clarity and can impart a certain emotion to the viewer–but the absence of eyes in my work alludes to the puzzling nature of the paradox. However, In place of the eyes is a black hole–the focal point of the piece—which encapsulates the mysterious, unpredictable nature of information loss, much like how anomalous diffusion deviates from standard physical models.

Edmund Harriss

Gradient of grain is a slice of an oak tree, carved by CNC along curves consistently at right angles to the grain. The resulting piece (this is 1/17) thus depends on the particular growth of that tree. 

This series grew out of other work where I was creating geometric objects (such as the Barth sextic) from wood. As a material the wood brought character and beauty to the pieces, but the geometry was imposed. Using the natural geometry of the wood (its grain) this piece instead is a conversation. 

The anomalous patterns in the grain are directly tied to how the tree grew and are thus a reflection of the story of this particular tree, that grew just yards from my workshop. The grain lines are also the level sets of the age of the tree, thus by carving at right angles the way that the tree grew is revealed, as is the mathematics of the gradient vector field lying at right angles to the level sets. 

The resulting piece thus explores how stochatic natural processes are recorded in the geometry of a tree and how they can be revealed and explored using mathematics.

Ankita Hazra (Entry 1)

This image showcases an intricate, glowing display of fungal-like formations, arranged in a structured yet organic manner. The circular patterns, with their radiating, petal-like gills, evoke the appearance of bioluminescent mushrooms or coral growths, glowing in rich hues of blue, purple, and gold against a dark background. These formations resemble mycelial colonies, expanding through stochastic yet constrained diffusion processes.

Mathematical Interpretation:

● Stochastic Growth & Diffusion: The dispersed structures suggest random yet bounded diffusion, akin to anomalous diffusion in complex environments. The varying sizes indicate heterogeneous diffusion rates, where spatial constraints influence growth.

● Fractal and Geometric Complexity: The intricate gill-like structures exhibit self-similarity, a hallmark of fractal formations. Their repetition aligns with power-law distributions, commonly seen in physics, ecology, and material science.

● Network-like Interactions: The interconnected formations mirror mycelial networks, governed by diffusion-driven expansion and environmental feedback loops. Similar patterns emerge in stochastic optimization, where adaptive search strategies mimic fungal resource-seeking behavior.

Conceptual & Artistic Impact:

The bioluminescent glow enhances the surreal, dreamlike quality of the piece, evoking both natural and computational processes. The contrast between soft, organic textures and sharp, geometric symmetry embodies the tension between chaos and order—a defining feature of stochastic systems and anomalous diffusion.

Ankita Hazra (Entry 2)

This image presents intricate, glowing formations resembling fungal colonies, unfolding through complex yet structured diffusion. The patterns suggest stochastic growth mechanisms, where randomness, environmental constraints, and self-organization shape the emergent structures.

Mathematical and Biological Interpretation:

1. Stochastic Growth and Morphology:

The branching structures resemble fungal networks or microbial colonies, expanding through probabilistic processes influenced by resource availability and spatial constraints.

2. Anomalous Diffusion in Biological Systems:

The formations exhibit non-trivial spatial interactions, mirroring how mycelial networks spread via constrained yet adaptive movement. Some clusters display long-range correlations, akin to anomalous diffusion in porous media.

3. Fractal and Nonlinear Dynamics:

The glowing filaments and radiating structures resemble fractal networks, characteristic of self-organized diffusion. This parallels Lévy walks, where organisms alternate between local exploration and long-distance movement, optimizing resource discovery.

4. Diffusion-Limited Aggregation:

The patterns align with diffusion-limited growth models, where particles deposit randomly and form dendritic, fractal-like structures, as seen in crystal formation and bacterial colonies.

5. Computational and Theoretical Insights:

These structures mirror Monte Carlo simulations of random walkers in constrained spaces, informing statistical physics, machine learning, and optimization models.

Conclusion:

This image beautifully visualizes the interplay between randomness and structure, offering insights into biological, physical, and computational interpretations of anomalous diffusion.

Ankita Hazra (Entry 3)

Title: Abstract Diffusion: A Visualization of Stochastic Growth           

This digital artwork presents an intricate, fractal-like composition, potentially representing stochastic or anomalous diffusion processes.

Analysis:

Color & Contrast:

● Deep blues and purples evoke a cosmic or microscopic atmosphere.

● Bright golden and cyan bursts contrast with the dark background, highlighting key focal points.

Structure & Composition:

● Organic, branching formations resemble fractal structures commonly found in natural systems.

● The interconnected golden bursts suggest nodes in a network, possibly depicting diffusion events or stochastic activity.

Mathematical & Scientific Interpretation:

● The artwork may symbolize anomalous diffusion, where some regions expand rapidly (light bursts) while others remain constrained (darker areas).

● Fine, web-like strands radiating from the golden bursts resemble random walks, a fundamental concept in stochastic models.

Potential Connection to Stochastic Diffusion:

● The interplay of randomness and structure aligns with principles of anomalous diffusion.

● Clustered golden bursts could represent high-activity regions or "trapped" particles in an uneven diffusion space.

● The transition between colors and densities may signify variable diffusion rates, confinement, or environmental interactions.

This artwork offers a striking visualization of the balance between chaos and order, reflecting key principles of stochastic growth and anomalous diffusion. )

Julio Hernández (Entry 1)

Title: Sweet Collision – Entangled Paths of Anomalous Motion

Sweet Collision, The Dynamics of Chaotic Interactions; embodies the mathematics of anomalous diffusion, where movement follows unpredictable yet statistically structured paths. The interplay of colors and forms represents stochastic motion, particularly Lévy flights, where rare but large displacements punctuate smaller, localized steps. This pattern, found in natural and artificial systems, governs phenomena such as molecular transport in turbulent flows, the erratic paths of foraging animals, and stock market fluctuations. The swirling composition reflects super diffusion, a process in which transport occurs faster than standard Brownian motion, influenced by memory effects and long-range correlations. The visual energy within the piece mirrors the way particles spread through disordered environments, where interactions between different scales create emergent patterns. The structured chaos depicted here also evokes stochastic resonance, where noise paradoxically enhances signal detection, highlighting the counterintuitive role of randomness in ordered systems. By capturing the complex balance between unpredictability and determinism, this artwork transforms mathematical abstractions into an intuitive visual experience. The tension between collision and dispersion, order and disorder, mirrors the governing principles of anomalous diffusion, revealing the intricate, often hidden, mathematical frameworks underlying seemingly chaotic motion. Through color and form, it visualizes how stochastic processes shape the fundamental dynamics of nature.

Julio Hernández (Entry 2)

Title: Stochastic Horizons – Patterns in Unpredictability

Stochastic Horizons, Patterns in Unpredictability; is a piece that explores the non-uniform propagation of movement in stochastic systems, capturing the irregular yet structured nature of anomalous diffusion. Unlike classical diffusion, where motion is independent of past states, this artwork embodies non-Markovian dynamics, where history influences progression. The fragmented forms depict Lévy flights, characterized by sudden, large displacements interwoven with localized movement patterns seen in diverse contexts, from protein dynamics in cells to financial market fluctuations. The layered structures evoke a multifractal geometry, where self-similarity exists across multiple scales, mirroring transport through porous media and biological tissues. The unpredictable color shifts symbolize the contrast between randomness and mathematical determinism, where disorder reveals deep, underlying structures. The transitions between dense and sparse regions mimic transport in disordered systems, where obstacles create irregular yet statistically predictable pathways. By visualizing how anomalous diffusion manifests in nature, this piece transforms abstract mathematical principles into a tangible sensory experience. It reflects how patterns emerge from apparent chaos, demonstrating that stochastic processes are not mere randomness but fundamental to the organization of complex systems. The composition invites the viewer to explore the hidden order within unpredictability, making the invisible forces shaping our world perceptible through visual expression.

Julio Hernández (Entry 3)

Title: Introspective Landscapes of the Mind – Cognitive Diffusion in Neural Networks

Introspective Landscapes of the Mind, A Fractal Vision of Thought; translates the mathematics of cognitive processes into visual form, representing anomalous diffusion within neural networks. Unlike classical diffusion, where signals spread uniformly, brain activity follows fractional dynamics, influenced by memory effects and long-range correlations. The swirling structures evoke Lévy flights, where sporadic, large jumps characterize information flow—patterns observed in synaptic transmission, search strategies, and thought patterns. The interconnected branches suggest self-organized criticality, where small perturbations can trigger cascades of neural activity, similar to how minor stimuli lead to complex cognitive responses. The contrasting density in the composition reflects multifractal structures within the brain, where different regions exhibit distinct yet interdependent diffusion properties. The interplay between structure and disorder mirrors stochastic resonance, where noise enhances signal propagation, revealing how randomness is integral to perception and decision-making. By capturing these abstract processes visually, this piece makes  invisible mechanics of thought more tangible. It transforms complex mathematical models into an intuitive experience, demonstrating how anomalous diffusion governs not only physical systems but also the workings of consciousness. Through color and motion, the piece invites viewers to reflect on how stochastic patterns shape our understanding, creativity, and awareness, revealing the mathematical essence of thought. 

Frankie Higgs

Video https://drive.google.com/file/d/1lAgP7ftnIkJY0PD2am4tJzOEU3tX5HyS/view?usp=sharing

Bacteria in a petri dish begin to grow in the shape of a disc, and if there are many competing colonies they will bump against each other and divide the space between them. When all colonies grow at the same speed, the resulting pattern is called a Voronoi tessellation, a classic model in random geometry.

What this video shows is the effect of colonies having very different growth speeds. At the start of the video we show the pattern from all the speeds being very similar - the space is divided between thousands of different colonies. As the video continues we exaggerate the difference between the slowest and fastest growth rates, and we end up one colour covering most of the screen: the most well-adapted strain has occupied almost all the available space, smothering its slower competitors before they are more than a handful of cells.

We get a very different pattern from the well-understood Voronoi tessellation. The growth speeds are an example of heavy-tailed random variables, where we have a "big jump" phenomenon: the speed of the fastest colony is greater than all the other speeds added together.

Cy Hilario

From an original artwork, it can become a new one with the use of replicating a part of the image (reflecting process) in different angles (concept of geometry) that create a certain style by adding elements (mathematical pattern). It goes to show that art and mathematics go hand in hand to be able to produce something of value and meaning.

Michael Hobbs

I wished to interrupt the overall homogeneous structure of the Gray-Scott model by braking its symmetry with a simple parquet deformation. When I chose to copy the result onto paper the uneven surface texture also introduced an element of randomness to the drawing. 

Tina Hojati

The painting is named "The Unsolvable Equation". It. The contrast between dark and light represents internal struggle as if the mind is trapped within itself.

The purple streak in the brain suggests an outpouring thought while solving mathematics, like the frustration and intensity of tackling unsolvable and paradoxical problems. Math which is often seen as structured and logical, sometimes confronts limits much like Gödel’s incompleteness theorems and unsolvable equations. This painting visualizes this suffocation of analysis. The brain pushing to break through that intellectual barrier, grasping at solutions which may remain just out of reach no matter the struggle. The hands reinforce the struggle while the mind is both reaching for and resisting thoughts like being trapped in an infinite loop of problem solving.

Dalion Huang

Link https://drive.google.com/file/d/1Jzx7X0M65oey44WpbM8zVO7FDquFn9Io/view?usp=sharing

Everything in the world is chaotic, yet many small things in life seem to maintain order and regularity. The Fourier transform could mean following the veins of order and pattern, constantly approaching and widening the frequency distribution, making events increasingly precise. So far, we are still like the summer cicada that knows nothing of spring.

Helen Hughes 

Title: Sacred Love

My Paper Mosaic artwork beautifully illustrates the interplay of mathematics. 

This paper mosaic artwork exemplifies the interplay of probability theory and art through its structured yet unpredictable arrangement of tiles. The seemingly random distribution of paper squares reflects an underlying order, reminiscent of diffusive processes in probability, where individual particles (or in this case, tiles) follow stochastic paths while contributing to a coherent visual form.

The irregularity of the tile shapes and their varying colour densities parallel interacting particle systems, where local randomness results in large-scale patterns. This echoes how random networks form in nature…. akin to neural connections or social interactions… suggesting a balance between chance and design. The artwork also resonates with the concept of reflecting processes: each tile’s placement influences its neighbours, much like probabilistic models in physics, where particles collide and redirect.

Musab Hussain

This artwork explores the fascinating concept of interacting random walks, a mathematical idea that describes unpredictable paths weaving and shifting through space. Each glowing line represents a unique journey — some flowing smoothly, others jagged and chaotic — yet all connected by subtle, hidden patterns. Bright nodes appear where these lines meet, symbolizing moments where randomness gives rise to unexpected structure and order.

The color palette of cool blues, deep purples, and silvers was chosen to create a calm yet energetic mood. These colors reflect the balance between quiet motion and sudden bursts of activity. The cosmic-inspired background adds depth, suggesting an endless space for these random paths to unfold — much like particles drifting through the universe or electrical currents finding their way.

The flowing lines resemble constellations, tangled threads, or branching rivers, blending chaos with moments of surprising harmony. This piece shows how mathematics isn’t just about numbers — it’s full of movement, beauty, and creativity.

By turning abstract ideas into something visual and expressive, this artwork invites viewers to reflect on the unexpected ways patterns emerge in nature, science, and even in our daily lives. It’s a reminder that even in chaos, there’s often a hidden sense of order waiting to be found.

Sarah Hussein

A mesmerizing abstract painting with swirling, fractal-like patterns symbolizing the unpredictable flow of stochastic diffusion. Glowing particles and interconnected curves create a sense of hidden mathematical structure.