Letter P

Yeganeh Panahi joo (Entry 1)

“Once upon a lifetime” is a series of AI generated images that mimic anomalous diffusion of time, where patterns emerge from the way time, scale and form interact. They are neither fully random nor entirely predictable. 

The generated patterns are derived from blends of time-related scientific diagrams in different scales: Penrose diagrams (space time structure), Van Allen belts (Planetary radiation fields), time-dimensional phyletic diagrams for the evolution of organic matter and organisms for the planet Earth (biological time), and microscopic image of calcite crystal in a coarse grained marble (mineral growth over time). 

Like particles in constrained environments, time exhibits random walks_ it shifts, bends, and loops, shaped by forces like gravity, surroundings, and adaptation. The AI’s algorithmic blending reflects how complex systems—be they physical, biological, or temporal—produce intricate, self-evolving geometries beyond simple causality. Each image contains elements—whether in form or colour—drawn from microscopic images of calcite crystals, the building blocks of marble. Marble itself forms over millions of years under heat and pressure, its crystalline structure growing through processes of transformation and constraint. The images capture a sense of temporal refraction where deep time is shaped fractured and reassembled into ever shifting patterns.

Yeganeh Panahi joo (Entry 2)

In the early 19th century, as the Parthenon Marbles were removed from Greece, a parallel yet lesser-known story unfolded 2,000 miles away in Leptis Magna, Libya. Hoping to replicate the marbles’ reception, the British consul general in Tripoli persuaded the local governor to send Roman ruins to Britain as a gift for the Prince Regent. Unlike the Parthenon Marbles, these remains were met with indifference, left in the British Museum’s forecourt for eight years before being repurposed as a folly at Virginia Water—where they remain today.

This painting refracts these parallel narratives into a nonlinear exploration of time, memory, and history. It envisions time as an anomalous diffusion process—a force that does not flow evenly but disperses unpredictably, with refraction distorting its trajectory. The displacement of these ruins is not a linear event but a stochastically scattered sequence across landscapes and periods, folding into itself and creating cyclical echoes where past and present intermingle.

Through these fragmented yet interconnected narratives, the painting examines how history is shaped by time’s flow. Rather than a fixed record of the past, history behaves like a diffusive pattern that continuously reshapes itself, merging past and present into a dynamic, ever-evolving form.

Bianca Paraschiv (Entry 1)

Title: Echoes of Motion

"Echoes of Motion" (165x115 cm, acrylic and oil on canvas) explores the unpredictable nature of movement and transformation, mirroring the concept of anomalous diffusion. The composition embodies a dynamic interplay between constraint and release, where the figure’s hands act as both anchors and agents of motion—expressing tension, resistance, and an urgent search for escape. The organic, fluid textures suggest a complex environment shaped by invisible forces, akin to particles navigating irregular landscapes, encountering barriers, reflections, and feedback loops that alter their trajectories. Through abstraction and figurative fragmentation, the work visualizes the struggle of motion against confinement, capturing the essence of stochastic paths that never fully repeat yet remain bound by the memory of past movement.

Bianca Paraschiv (Entry 2)

Alpha & Omega ( 64x50 cm, mixed media on paper ) visually embodies the cyclical and stochastic nature of existence, invoking the principles of diffusion and its anomalies. The composition features the symbolic forms of beginning and end, intertwined yet separated, representing the eternal movement between order and chaos. The fragmented, evolving lines suggest the unpredictable nature of diffusion, where paths are altered by memory, reflection, and environment. The organic flow of shapes reflects particles that encounter resistance and feedback, each journey unique but tethered to the past. Alpha and Omega—acts as a metaphor for how forces of origin and culmination coexist in a state of constant motion, sometimes accelerating, sometimes slowing down, driven by unseen patterns and internal dynamics. This work examines how life’s beginning and end are not fixed but are continuously shaped by the chaotic, ever-changing forces of nature and existence.

Central to the piece is the iris, which serves as both a symbolic and visual focal point. The iris represents perception and insight, echoing the idea that understanding—like diffusion—is an ever-evolving process, shaped by internal and external forces. The concentric layers within the iris mirror the expanding and contracting nature of time, space, and consciousness, with each ring symbolizing a different phase of existence, influenced by feedback, reflection, and adaptive learning.

Bianca Paraschiv (Entry 3)

"Disrupted Continuum" explores the fragmented pathways of anomalous diffusion, where motion is neither linear nor predictable but shaped by structural constraints and dynamic shifts. The composition, with its interplay of geometric rigidity and organic disruption, evokes a space in flux—an architectural landscape subjected to the forces of time, memory, and adaptation.  

The distortions and layered transparencies suggest the unpredictable trajectories of movement through constrained environments, much like particles navigating through an irregular medium. The contrast between structured frameworks and chaotic fractures mirrors the way boundaries, feedback loops, and external forces influence diffusion processes, whether in physical systems, biological evolution, or human perception.  

Lines break, perspectives warp, and space folds in on itself, capturing the essence of diffusion beyond its classical form—where memory effects, spatial inhomogeneities, and feedback-driven deviations lead to unexpected outcomes. This visual complexity invites the viewer to consider the unseen forces that guide movement, decision-making, and the passage of time.

Mohammad Javad Pardakhteh (Entry 1)

The hexagonal mathematical pattern of a bee's hive starts from the bee's hive and gradually spreads all around, becoming a large and beautiful house.

Mohammad Javad Pardakhteh (Entry 2)

The Pythagorean tree pattern is a mathematical pattern that creates a world from small, repeating elements in the form of a beautiful, large tree, from which fruits grow and are surrounded by butterflies and birds.

Mohammad Javad Pardakhteh (Entry 3)

In nature, from trees to galaxies, there are many shapes that exhibit a flow of self-similar shapes. In mathematics, terms such as self-similarity have special meanings. If the entire structure is changed by a certain scale, it is self-similar. The resulting shape may be smaller, larger, rotated, or inverted; but it still looks like the original shape. Self-similarity means that the relative proportions between the shape's faces and interior angles remain constant. If an object changes unequally in one or more dimensions, then the change is self-dependent. In a self-dependent change, the interior angles of the shape or the relative proportions of the shape's faces may not be the same. The length, area, or volume of a fractal structure increases as it undergoes self-similar transformation. The golden ratio, as an example of a self-similar scale, has long been a useful tool for architects.

The golden ratio creates a spiral-like form from a self-similar rectangle. The goal here is to demonstrate a natural, self-learning dynamic system, like a human educating himself with a book.

Nirmala Patel

The world is full of beauty. Mathematical models can describe – besides regular shapes, symmetries and relationships – phenomena that show anomalous mathematical patterns. Such patterns, including fractals and the Fibonacci sequence, abound in nature. Complex interactions also throw up anomalous patterns. Mathematical models draw on probability theory to provide insights into these phenomena, which appear across a dizzying range of subjects: the flow of traffic and pedestrians, the flocking of birds, climate models, animal coat patterns, financial markets, the propagation of cracks, the movement of predators such as sharks and diffusion in cells. The painting includes a randomly generated network, where the modes were coloured according to the roll of a dice. Random networks are key to studying complex networks, such as social networks and neural networks. 

Deborah Pearse (Entry 1)

Title: Binaural Techno

This diptych explores similarity and difference through two panels of complementary and vibrant colours. Both panels interpret the same sound wave pattern distinctly: the first, acidic green, is rounded and fluid, suggesting an inner focus of order; the second, with its complimentary; a strong magenta pink, renders the pattern as angular and lively. They both connect through a dynamic, reflective interaction.

Inspired by techno music and individual rhythms and dispositions, this work visualises fusion and transformation. The shared pattern, though rendered differently, represents an evolving relationship, where initial order shifts to complex emergence. This visual interplay reflects mathematical principles of dynamic systems, while embodying emotional and relational dynamics. Like interacting mathematical elements, the panels illustrate these distinct visual forms, from a shared source, whilst suggesting potential for ongoing evolution.

Deborah Pearse (Entry 2)

From my Sound Signature Series, 'Convexity Yellow' adapts and scales a fundamental sine wave pattern found in nature, a recurring motif within this body of work. This adapted pattern is then subjected to a visible modification, envisioned as a spherical influence, disrupting the wave's inherent symmetry. The resulting adaptation to its structural network creates shifts in density, colour, and trajectory, visually demonstrating how hidden interactions can alter the form's essential framework.

Inspired by synesthesia, I aim to translate sound into visual fusions of form, colour, and texture. This work explores how natural mathematical patterns, like the sine wave, provide visual metaphors to explore effects on  complex systems and organisations. By visualising the wave's transformation, 'Convexity Yellow' investigates how our perception shifts in response to dynamic changes caused by influences on processes, revealing the unexpected complexity within elementary systems.

Varied hanging configurations, including revolving canvases, often employed in my diptychs and multiples, are used to continue to explore shifts in perception, literally reframing the artwork.

Deborah Pearse (Entry 3)

'Aquatic Synchrony' visualises the emergent patterns of a collective where individual movements coalesce into a dynamic network, echoing principles found in stochastic systems and anomalous diffusion. Part of my Fluent Networks series, this work explores an abstracted yet recognisable aquatic murmuration, depicting the inherent unpredictability and deep interconnectedness of self-organising systems.

Drawing from a lifelong fascination with interconnection and adaptation, and informed by David Bohm and David Peat's insights on the implicate order, this piece expresses the visible and subtle forces shaping these emergent patterns. Here, order arises organically from within, not through external control. Forms and structures dissolve and reform in continuous, fluid resonance, an instinctive choreography of cohesive transformation. This mirrors the non-deterministic pathways observed in anomalous diffusion.

'Aquatic Synchrony' invites contemplation on how macroscopic order arises from microscopic stochasticity. The seemingly random movements of individuals contribute to a coherent, evolving whole, much like the probabilistic nature of anomalous diffusion. This artwork visually explores the emergence of complexity from underlying randomness, a concept central to understanding self-organising systems and their mathematical underpinnings.

R. T. Penwill

‘What are the chances?’ explores a range of mathematical themes through its depiction of the coin toss: a symbol of probability and randomness. The outcomes on the first two panels are deliberately chosen, challenging the assumption of pure randomness and suggesting that even processes governed by probability can be shaped by human intention. The arrangement of coin faces poses two subtle but persistent questions beyond the title: the chances of what, as measured by whom.

The sequential layout reflects a narrative of time. The first two panels present fixed outcomes of past coin tosses, while the blank space of the third panel represents the open uncertainty of the future. The viewer, occupying the present, finds themselves metaphorically positioned between the second and third panels. This liminal space emphasises the transition from what has already occurred to what is yet to come. The visible grain of the wood beneath the painted surface, with its distinct rings, further reinforces this temporal dimension. Its natural irregularities mirror the unpredictability of natural systems, while its concentric patterns act as a subtle metaphor for the passage of time, marking the accumulation of years and echoing the interplay of past, present, and future within the work.

Pooja

Cross-stitch relies on a grid, which is fundamental to coordinate geometry. The fabric acts as a Cartesian plane, with warp and weft threads defining the x and y axes.

Aida cloth, a common cross-stitch fabric, is a perfect example of this grid, with evenly spaced squares.

"Fabric count" is a measure of threads per inch. This is a linear density measurement.

For example, 14-count Aida means there are 14 squares (and thus, 14 potential stitches) per linear inch. This establishes a scale for the project.                                                            

Cross-stitch patterns are essentially discrete functions, mapping coordinates (grid squares) to color values.

Each square on the chart corresponds to a specific stitch, and the symbol within the square indicates the thread color.

Symmetry and repetition are common in cross-stitch patterns, which can be analyzed using group theory. 

The cross-stitch itself is a basic geometric shape, forming an "X."

Complex patterns are created by combining these basic shapes, and geometric principles like symmetry, translation, and rotation are often employed

Casement fabric, like all woven textiles, involves interlacing warp and weft threads. The weaving pattern can be described using mathematical concepts like:

Periodicity: The repeating pattern of thread interlacing.

Matrices: To represent the over and under nature of the woven threads.

The density of the threads, or thread count, again relates to linear density, and effects the fabrics opacity, and strength.  

Melvyn Poore

Thousands of straight lines transform before your very eyes! Here is power waiting to explode! The longer one looks, the more the straight lines turn into a mass of swirling currents. Look closely for the surface layer! Is this how CERN looks inside?

This image was generated from thousands of randomly-generated {x, y, z} co-ordinates which are joined together - in the order they are generated - to form a three-dimensional object. The color, transparency and width of the lines are also selected and applied by the same random process.

The co-ordinates are calculated within a unity cube and the other parameters are subject to boundary limitations given by the user (yes, subjective decisions). 

After this first, generative stage, scaling, rotation and camera position are used to search for 'best' results: also a subjective stance.

John Dave G. Poot

This artwork is constructed using a two-point perspective grid, creating a structured spatial framework. Within this grid, four distinct patterns, including a blank space, were predefined. A random number generator determined the placement of these patterns across the grid, assigning each block an outcome.

The result is a composition that follows a mathematical process—balancing structured perspective with stochastic placement. The perspective grid provides depth, while the randomized patterns introduce variation within the constraints of the system. The repetition and alternation of shapes create an interplay between order and unpredictability, reflecting concepts found in modular arithmetic and pattern anomalies.

This approach highlights how mathematical processes can generate structured yet varied visual outcomes. By using predefined elements and chance-based selection, the piece explores the relationship between systematic design and randomness in composition.

Lokanath Pradhan 

Video https://drive.google.com/file/d/1q6q5ZqA2A5-q0LJX58EsNKYBxNflnfrQ/view?usp=sharing

Title: Transformation of Landscapes ‚ A Mathematical Perspective

My work investigates the unpredictable yet structured evolution of urban landscapes through the conceptual lens of mathematical irregularities. Deeply influenced by my migration from Odisha to Delhi and my academic journey in China, I have observed how cities expand, shift, and adapt over time. These transformations resonate with mathematical phenomena such as stochastic processes, interacting particle systems, and anomalous diffusion, which reflect how urban environments evolve both organically and systematically.

This body of work draws inspiration from fluid dynamics, diffusive systems, and random networks, blending the aesthetics of precision with the disorder of entropy. The carved surfaces, with their varying elevations and textures, generate kinetic depth that changes with the viewer's position, evoking a dynamic experience similar to navigating through urban spaces.

By embedding these abstract mathematical structures into tangible, spatial forms, the work makes visible the often-invisible forces that shape our built environments. It aims to reflect the fragile equilibrium between chaos and control, growth and decay. Ultimately, this project serves as a bridge between scientific principles and artistic intuition‚ inviting the viewer to contemplate the underlying logic of the world we live in.

Scott Proctor (Entry 1)

The Navier-Stokes equations describe the motion of fluid substances such as air, water, and smoke. In this image, the behavior of moving smoke is governed by these equations, capturing both laminar and turbulent flows. The intermingling smoke elements visualize the interplay between mathematical precision and artistic visualization, revealing the hidden beauty of fluid motion, seamlessly blending scientific rigor with photorealistic artistry. The use of precise lighting emphasizes the contrasts and depth, creating a striking, modern composition that aligns with the theme of anomalous diffusion.

Different sources of smoke create heterogenous diffusion -- this non-uniform dispersion results in anomalous diffusion, where the mean squared displacement (MSD) of particles follows a power law as opposed to normal (Fickian) diffusion, in which particles are assumed to spread out in a medium in a predictable manner, following Brownian motion, where the MSD of particles grows linearly with time.

Scott Proctor (Entry 2)

Waves in water are dynamic disturbances that travel through the ocean, rivers, and lakes due to wind, tides, or geological activity. These waves exhibit complex behaviors, from smooth, rolling swells to chaotic, turbulent breaking waves. Their motion is governed by the Navier-Stokes equations, which describe the motion of fluid substances such as air, water, and smoke. These equations balance forces such as pressure, viscosity, and inertia, providing a mathematical foundation for understanding wave dynamics.

In these images, the behavior of waves moving in water is governed by these equations, capturing both laminar and turbulent flows. The intermingling wave elements visualize the interplay between mathematical precision and artistic visualization, revealing the hidden beauty of fluid motion, seamlessly blending scientific rigor with photorealistic artistry. The use of precise lighting emphasizes the contrasts and depth, creating a striking, modern composition that aligns with the theme of anomalous diffusion.

Scott Proctor (Entry 3)

Turing patterns, named after the mathematician Alan Turing, are nature's way of creating structured, repetitive designs without any central control. These patterns emerge from a mathematical process called reaction-diffusion, where two substances spread and interact at different rates — one activating a process while the other inhibits it. This natural algorithm leads to strikingly complex yet predictable formations.

Nature is filled with mesmerizing patterns that seem too perfect to be random, yet too unpredictable to be purely designed. That is where Turing patterns come into play across domains as varied as animal coats and skin, desert sand dunes, coral growth and sea shells, and bioluminescent ocean swirls, amongst other phenomena.

These images not only illustrate reaction-diffusion systems but also capture the essence of anomalous diffusion in nature. These artistic interpretations serve as a bridge, making intricate mathematical phenomena accessible and engaging to a wider audience, thus merging scientific insight with artistic creativity.