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Matteo D'Achille
Matteo D'Achille
This pendant is crafted from a unique sample of the *zero cell* in the **ideal Poisson–Voronoi tessellation (IPVT)** of 3D hyperbolic space, $\mathbb{H}_3$. It merges two forms of beauty: the visual elegance of a shape reminiscent of a faceted gem, and the mathematical grace of a structure born from pure randomness.
In the low-intensity limit of the Poisson–Voronoi process, the nuclei—random points sampled in hyperbolic space—accumulate on the Gromov boundary (the ideal "sphere at infinity" in the Poincaré model). This produces a random, yet isometry-invariant decomposition of space into infinite cells, each pointing uniquely toward infinity.
The pendant represents one such cell, the one containing the origin. Its singular "end" is where the chain attaches—via a hand-crafted silver infinity symbol—evoking its asymptotic direction. The collar encircling the neck symbolizes the Gromov boundary itself.
Each jewel is a one-of-a-kind snapshot of this infinite, abstract structure: a tangible artifact from a world shaped by pure geometry and chance, yet almost surely beautiful.
Reference: D’Achille, M., Curien, N., Enriquez, N., Lyons, R., & Ünel, M. (2023). Ideal Poisson-Voronoi tessellations on hyperbolic spaces. arXiv 2303.16831
Rajenki Das
Rajenki Das
When I think of depicting diffusion, I often picture ink blooming in water. Diffused Blues captures this idea showing the natural process of diffusion where the blue pigment is guided by the flow of the water. This raises questions on how the density of solvents can determine the flow of the pigment, thus shaping the final pattern in ways that may or may not be predictable.
Though only one shade of blue was used, the variation in water content forms layers of tone and intensity, creating depth through nothing more than chance and movement. I added a touch of red to highlight the interplay of colours and media- introducing further uncertainty in how and to what degree they blend. The spreading of colour doesn’t follow brushstrokes but instead bleeds into surrounding areas, following its own path. This also reflects on how meaning can emerge from the unexpected.
In the end, this uncertain process of movement and mixing of coloured pigments through the flow of water has created an abstract which to me, resembles the northern lights or perhaps a forest fire. What do you see?
Shohel Das
Shohel Das
The three architectural masterpieces exemplify the profound relationship between mathematics and art, showcasing symmetry, geometric precision, and sacred proportions.
Islamic, Persian, and Buddhist designs all rely on intricate tessellations, radial symmetry, and fractal-like recursion to create visually harmonious spaces. The mosque ceiling’s geometric latticework is a testament to Euclidean geometry, employing star polygons, interlocking tessellations, and Muqarnas vaulting, forming an infinite pattern of repeating motifs. The Persian courtyard features pointed arches and hexagonal mosaics, using reflection and translation symmetry to create depth and continuity, while its vanishing point perspective aligns with projective geometry. The Buddhist temple hall, dominated by a golden mandala ceiling, embodies sacred geometry, where recursive fractals and the golden ratio structure its intricate carvings, reinforcing themes of cosmic balance and harmony.
Despite cultural variations, these spaces share a mathematical foundation, utilizing repetition, proportion, and symmetry to evoke a sense of transcendence. Whether through the infinity of Islamic tessellations, the ordered progression of Persian arches, or the recursive balance of a Buddhist mandala, each of these architectural wonders exemplifies the universal language of mathematics in art, reflecting both aesthetic beauty and spiritual significance.
Sevda Demir
Sevda Demir
Every action is a special case, seemingly organized, of the turmoil at its origin. We are swept up in a maelstrom that has its roots in the beginning of time, and the fact that this maelstrom has taken on the appearance of order is only to better grab us and drag us along...
Chaos is being oneself and rejecting everything learned.
Life is always in turmoil. A monotonous loss of light, a dull scattering in the night
Moments follow one another.
A flat absolute where nothing prevents things from spinning around themselves in pursuit of their own fall. Life is created in delirium and dissolved in distress.
The nothingness that causes actuality to continue is prior to all absolutes.
“Fifty-nine seconds of each of my minutes”
I envy the object... The grace of matter and dullness... Of motion and my dreams
Dariya Dimova
Dariya Dimova
My artwork represents how artistic concepts can be used to create anomalous mathematical, unexpected patterns that are not normally seen in our everyday life. My drawing consists of two asymmetrical spheres balancing each other surrounded by symmetrical squared pattern background in different colours. The combination is unusual, and at the same time captivating. By looking at the picture, one can spend some time contemplating at the mathematical shapes/forms, and their deeper meaning.
Christian Dimpker
Christian Dimpker
Stochastic music is a compositional technique that uses random processes to generate musical elements. It is inspired by probability theory and statistics, and it involves applying mathematical algorithms to create melodies, harmonies, rhythms, and other aspects of music. Greek composer Iannis Xenakis is one of the pioneers of this approach. In N. 33 Holistic notation study I {Granular visions}, this approach serves as the basis for the organisation of of the visual and sonic layers, the effects and dynamic levels while taking the sound synthesis technique referred to granular synthesis - which was also first discovered by Xenakis - to the visual level. The piece takes a look into the greatest expanse and the finest microscopy. It fuses images and sounds that elude the lazy eye and ear, constantly escaping them. Visitors view the work through jeweller's loupes, which – attached to a microscreen – add an extra layer of blurry deception and fuse the screen with the piece. The images and sounds cannot be pinned down because they only take shape in the granular range, usually between 5 and 80 ms, rarely longer. By doing so, the template evolves to a substantially new work, opens up abstract worlds while the flood rattles faster than the brain.
Link to the score https://www.universaledition.com/en/Works/N.-33-Holistic-notation-study-I-Granular-visions/P0271766
Ana Djurdjevac
Ana Djurdjevac
Title: The Art of Instability
In this artwork, I explore the parallels between mathematical modeling of anomalous diffusion and the physical unpredictability of the pouring painting technique. Pouring involves using fluid pigments in a liquid state and letting them flow freely across the canvas. The artist has only partial control—neither the exact path nor the blending of colors can be fully predicted. This spontaneous behavior closely mirrors the essence of anomalous diffusion, where particle transport deviates from classical diffusion due to memory effects, long-range interactions, or stochastic influences.
To ground this analogy, I drew inspiration from simulations in the paper Fluctuating Hydrodynamics of Electrolytes at Electroneutral Scales by Donev et al. Specifically, the artwork visually reflects the asymmetric growth of convective fingering patterns in a Hele-Shaw cell—a phenomenon driven by gravitational instability and a neutralization reaction under stochastic fluxes. The color fields in the painting correspond to the evolving density of Na⁺ ions, depicted at both initial and later times.
Anomalous diffusion plays a central role in these dynamics, altering how reactive species spread and interact. It enhances the irregular, asymmetric development of the fingering structures—much like the unpredictable spread of paint—capturing the interplay between randomness, instability, and reactive transport.
dN eQ
dN eQ
Light is electromagnetic radiation that is perceived by the human eye. Light is often used to refer to any optical radiation, that is, electromagnetic radiation whose wavelengths lie in a range with approximate boundaries from units of nanometers to tenths of a millimeter. In this case, the concept of "light" includes, in addition to visible radiation, both infrared and ultraviolet radiation. Light can be considered either as an electromagnetic wave, the speed of propagation of which in a vacuum is constant, or as a stream of photons – particles.
When all the waves are reflected, we see white. If the light is not reflected, then we see black.
Diffusion of light this is the reflection of a luminous flux falling on a surface, in which the reflection occurs at an angle different from the incident angle and taking into account not necessarily the plane of the incident radiation and the normal to the surface (specular reflection).
Katerina Dounavi
Katerina Dounavi
This video deals with randomness and non-randomness in the creation of an artwork, with probability theory at its core. It resulted from the segmentation of three images that are digital representations of a three-part physical painting. The fragments of the images are repositioned differently in order to produce each frame of this video. The selection of the fragments is determined by their RGB resolution, which follows a Gaussian distribution. Specifically, as the thresholds of the distribution change incrementally, the images selected to produce each frame change. As time passes and filtering becomes stricter, some images appear more than once in the same frame. This has the effect of creating an anomaly in the uniqueness of the selection, which tends to create pattern effects. Thus we move from seemingly more random and visually anarchic images to more predictable ones with recurring elements. This process is reversed and repeated as the video plays in a loop. One could therefore say that random processes are being performed, as the abstract visual effect does not predispose to anything meaningful but in fact the acting forces are anything but random; they are simply behind the scene, inviting the viewer to discover them.
Alain Dupet (Entry 1)
Alain Dupet (Entry 1)
My artwork visually explores the concept of anomalous diffusion. A central fractal structure, reminiscent of a Julia set, dominates the canvas, symbolizing the irregularity and self-similarity often observed in these systems. Swirling, turbulent patterns, evoking fluid dynamics, overlay the fractal, capturing the chaotic and unpredictable nature of the process. Subtle digital elements, such as interacting particles, are integrated, hinting at the underlying mathematical models. The interplay of vibrant colors and dynamic forms invites viewers to contemplate the beauty and complexity of stochastic systems.
Alain Dupet (Entry 2)
Alain Dupet (Entry 2)
My artwork is a visual representation of the intricate and unpredictable nature of diffusion processes that deviate from the standard Brownian motion. The artwork is a kaleidoscope of colors and patterns, creating a visual symphony of chaos and order. The vibrant hues and psychedelic patterns intertwine and evolve in dynamic swirls, showcasing a complex visual tapestry. The intricate fractals and delicate, interwoven designs break down into a chaos of patterns and colors, capturing the essence of anomalous diffusion. The interplay of light and shadow adds depth and complexity to the image, creating a visual richness that draws the viewer into its fascinating intricacies.
Alain Dupet (Entry 3)
Alain Dupet (Entry 3)
"Anomalous Weave: Reflections in a Kinetic Network" is a digital artwork visualizing stochastic systems and anomalous diffusion. It features a dynamic network of irregular nodes and lines, representing interacting particles. Simulated particles move anomalously, leaving luminous trails that depict their unpredictable paths. Reflecting nodes alter these paths, showcasing reflecting processes. The animation creates a kinetic experience, highlighting the system's evolving nature. A color palette of blues, purples, and oranges conveys energy and randomness, with bright flashes marking key events. This piece aims to visually bridge abstract mathematical concepts from the Isaac Newton Institute's program.
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