Letter J

Orla Jackson

‘Blue Blanket’ - Brownian motion in blue – ink diffusion in wet paper.

When I start inking a fresh batch of Japanese papers, for some reason, there is an initial sense of trepidation, I find myself holding my breath. Perhaps it’s because I place so much value on the materials; they are expensive and precious to me. But once the first few drops of ink hit the paper, I exhale, relax, and realise the irony—I have little control over this process, I surrender.

There is an intimate beauty in the first moments when droplets of ink touch wet paper, it spreads in all directions from highly concentrated drops to areas of lower concentration and beautiful patterns emerge. Dry paper does not allow the ink molecules the same freedom. Instinctively I cease dropping ink, if I add too much, the watery edges vanish, and the colour distribution becomes more uniform. I want to hold onto the unpredictable patterns, reminiscent of the ever-changing movement of the sea and sky.  

Paradoxically, once dry, I regain control by carefully measuring and creating a uniform grid, transforming the papers into a cloth-like patchwork blanket. This blanket reflects the dual themes of comfort and the recurring journeys of many Irish people, including myself, across sea and sky.

 Tharani Jaiprakash

The artwork's relationship with the concept of anomalous mathematical patterns is profound and thought-provoking, serving as a visual embodiment of these unexpected deviations in otherwise predictable systems. Anomalous patterns, in mathematics, refer to irregular or surprising deviations from established trends, often revealing hidden complexities or insights within data or natural phenomena. 

This idea is well-reflected in the artwork through its seemingly chaotic yet structured design. The interplay of irregular shapes and unexpected symmetries mimics how anomalous patterns arise—unexpected disruptions within an otherwise orderly framework. The artwork highlights how such irregularities can appear random but are often governed by underlying principles waiting to be unraveled.

For instance, anomalies are frequently studied in disciplines like statistical analysis, where deviations from expected distributions can lead to groundbreaking discoveries. Similarly, the artwork's unpredictable elements could symbolize such moments of mathematical serendipity, challenging viewers to seek the hidden logic within the apparent randomness.

Moreover, the dynamic use of color and motion in the piece evokes the nature of chaotic systems, where anomalies often occur. These systems are studied in chaos theory, where minor deviations can lead to significant and sometimes beautiful complexities, a notion mirrored in the artwork’s design.

Ultimately, the artwork encourages appreciation for the beauty and importance of anomalies in mathematics. Far from being mere disruptions, these patterns often offer critical insights and showcase the elegance inherent in the unexpected. It is a vivid celebration of finding meaning within the unpredictable.

Jonas Jalowy (Entry 1)

Title: A random tessellation of fluid dynamics 

We see a random Delaunay triangulation based on a non-Poisson point process, each randomly displaying different aspects of the ocean and coast (one of which actually is a 'Poisson'). The gradient flows from deep ocean to sandy beach.

(Acrylics on canvas)

Jonas Jalowy (Entry 2)

Title: A concrete Fibonacci owl

In the lost chapter of [Concrete mathematics by Knuth, Patashnik, Graham. 1988], we study a _concrete_ realization of the Fibonacci spiral (see section 6.6) which _abstractly_ takes the shape of an owl.

Shaped from concrete, and oak wood for the feet.

Buddy James (Entry 1)

Link https://x.com/i/grok/share/HXAbX8xJBVH4qlWAVMAW0ZaLE

This conversation explores the formation of the HH 30 protostar in the Taurus Molecular Cloud, as observed by the James Webb Space Telescope, through the lens of the "Buddy James Dougherty set," a hypothetical framework initially tied to z-pinch star formation and later redefined as magnetohydrodynamic (MHD) geometry. We began by relating HH 30’s protoplanetary disk and jets to a z-pinch model, where electromagnetic forces compress plasma, mapping the cloud’s 20-30 light-year expanse to filamentary pinch zones. Equations for magnetic confinement and jet dynamics were proposed. The discussion then shifted to MHD winds, aligning with mainstream astrophysics, where magnetic fields and rotation drive accretion and outflows. The Dougherty set evolved into parameters like magnetic field strength, disk radius, and angular velocity, fitting HH 30’s features (disk ~200 AU, jets ~400 km/s). Finally, a "Grand Unified Equation" was derived, balancing accretion energy with jet power and magnetic energy, encapsulating the MHD geometry’s role in HH 30’s evolution. This journey blends alternative and standard models, offering equations, proofs, and conjectures to interpret JWST’s stunning data, with the Dougherty set as a unifying geometric scaffold. The birth of a Star is indeed a diffusion process!

Buddy James (Entry 2)

Link https://x.com/i/grok/share/k8bbJGiDdzzFxzyhSIlmvNqN8

This exploration integrates nucleosynthesis, transmutation, active galactic nuclei (AGN), nucleogenesis, helical knots, and knot theory within the "Buddy James 'Dougherty Set,'" a geometric framework emphasizing helical, toroidal, and fractal structures driven by electromagnetic forces, as depicted in a detailed diagram (A-Y). The "Dougherty Set" reimagines these processes through principles, using knot-like topologies to enhance energy focusing across scales—from primordial nucleogenesis in helical vortices to transmutation in knotted plasma filaments, and nucleosynthesis in AGN jets reinterpreted as plasmoid quasars. We developed equations for each diagram, such as energy density for helical knots and transmutation rates, alongside proofs like knot stability in AGN jets. Experiments using the scientific method, such as testing nucleosynthesis in helical plasma, aim to verify these concepts. Future technologies, including the Helical Nucleosynthesis Reactor and Transmutation Forge, were proposed, with roadmaps outlining development from 2025 to 2050, costing $11.845B total. These innovations, leveraging electromagnetic and topological principles, could revolutionize energy, materials, and space exploration by 2050, challenging standard astrophysical models with the "Dougherty Set"’s visionary approach. These descriptions provide evidence of diffusion processes and more.

Buddy James (Entry 3)

Link https://x.com/i/grok/share/zvXGEd6F34jUUYkyIe9sATrMF

The concept of the "Dougherty Set," introduced by Buddy James, offers a fascinating geometric framework that could potentially unify the observations made by MIT researchers in their study of wave patterns across diverse systems, as detailed in the article from March 23, 2020, on MIT News (https://news.mit.edu/2020/growth-organism-waves-0323). The MIT team observed that ripples across a newly fertilized egg exhibit behaviors strikingly similar to wave patterns in seemingly unrelated systems, such as ocean currents, atmospheric circulations, and even quantum fluids. These ripples, emerging as spiral patterns that swirl, collide, and dissipate, suggest a "very universal wave pattern" underlying physical and biological phenomena. Integrating the Dougherty Set into this narrative provides a compelling lens through which to explore the cause of this universality. This showcases irregularity and anomaly of mathematical patterns on a universal scale.

Geraldine Jones

Video https://drive.google.com/file/d/1ZoicgnHuqYUqdxLUM4RBmVMWpX30KCCW/view?usp=sharing

The 2 pieces submitted cover aspects of mollusc morphology, the development of Pattern and Form through anomalous diffusion.

They both describe pattern and the use of visual guidelines to increase variously spaced Fibonacci number rows.

They are both based on Mobius strips, one with a wider space through the middle.

They are both tactile and can be manipulated, twisted, turned and explored so that the edge is always accessible.

The first piece has an edge which has reached the limit of accessibility, though it is still possible to access the entire hyperbolic edge.

The second piece can be more easily manipulated.

The diffusion is demonstrated in the visual pattern seen in developing guidelines around the edges of the 2 pieces.

The increase in form through a Mobius strip is a tactile experience of growth.

The aesthetics could be improved if the significant guidelines were to be removed but I think they are important at this stage to demonstrate the ideas behind them.

I myself have only recently discovered the beauty of mathematics through working with the team Forces in Translation and being given the opportunity to develop these and similar structures.

Ruta Jukonyte

This series investigates the unpredictable motion of particles through the lens of fluid dynamics, capturing the essence of stochastic systems and anomalous diffusion. These images depict shifting patterns formed by liquids of varying viscosities, revealing the interplay of randomness and structure in nature. Unlike classical diffusion, where motion follows predictable paths, anomalous diffusion unfolds in irregular bursts, creating intricate, evolving forms.

Through macro photography, I highlight the delicate balance between order and chaos—droplets suspended in motion, merging, dispersing, and reshaping in ways that feel both spontaneous and inevitable. These interactions mirror real-world stochastic processes, from molecular transport to turbulence, where uncertainty is not a flaw but an inherent characteristic.

The unpredictable, in the right light, becomes beautiful.