This series of ten photographs represents various mathematical concepts, with each image capturing the essence of a different mathematical idea or theory. From fractals and geometry to the abstract nature of infinity and chaos theory, each photo is designed to translate complex mathematical principles into visual metaphors. Some images specifically use colors to highlight contrasts and mathematical patterns, while others are captured in black and white to add depth and an introspective feel. The broken mirror in one of the images symbolizes the concept of symmetry and asymmetry, where the reflection of an object in a fragmented mirror represents the idea of broken symmetry in mathematical functions. Distorted patterns in another image reflect chaos theory, where small changes in initial conditions lead to vastly different outcomes, similar to the butterfly effect. In another photo, the concept of infinity is explored through repetitive patterns, emphasizing the endless nature of certain mathematical sequences. These photographs aim to evoke thought and curiosity, inviting viewers to explore the complex relationship between mathematics and visual representation, revealing the hidden beauty and complexity behind mathematical ideas.
This abstract drawing, made entirely with a black gel pen, turns quiet repetition into a kind of visual math. It plays with patterns, echoes, and variations—like a hand-drawn version of a statistical model unfolding in real time. No ruler, no plan, just rhythm and curiosity. Some marks repeat like data points in a trend; others break the pattern, like outliers refusing to behave. It’s a nod to probability, chaos, and the strange beauty of uncertainty. As shapes build and shift, the work begins to mirror how mathematical insight often sneaks in—through observation, variation, and sometimes, happy accidents. It’s a balance between structure and freedom, much like statistics itself: finding meaning not in one point, but in the space between many. This piece invites viewers to see math not as formulas, but as a living, breathing process—one mark at a time.
These artworks explore mathematical concepts such as randomness and phase transitions through geometric abstraction and spatial manipulation. The use of a principal rule based on an increased unit scale from 1 to 5 introduces a structured yet unpredictable rhythm, mirroring the concept of mathematical randomness. Although each unit follows a predefined progression, their spatial arrangement and overlapping symmetry create visual outcomes that feel random, yet logical.
The idea of phase transitions is reflected in the transition between structured symmetry and fractured space. The works move between order and disruption, embodying the thresholds at which transformation occurs. These visual shifts act like phase boundaries, where an ordered pattern suddenly gives way to fragmentation.
Parallel mirrors and unfolding symmetries add layers of recursive complexity, making the multidimensional nature of systems undergoing change. The tension between repetition and rupture becomes a metaphor for the fine line between equilibrium and chaos. Through this lens, the artworks become not only visual expressions but also conceptual models for understanding how randomness and transition shape both natural systems and human perception.
Nature is shaped by hidden mathematical structures, and this artwork explores anomalous diffusion and reaction-diffusion systems in the patterns found in landscapes. Inspired by Turing’s model of pattern formation, these images picture fields where floral and organic textures emerge from reaction-diffusion-like structures, reflecting the mathematical processes.
However, unlike classical reaction-diffusion, the patterns here exhibit irregularities and disruptions, mirroring anomalous diffusion—a process where movement is influenced by memory effects, spatial constraints, or external forces. In ecosystems, plant dispersion is rarely uniform; environmental factors create patchy, irregular growth.
The blending of structured and chaotic regions in the images symbolises the balance between order and randomness, a concept fundamental to probability theory and stochastic systems. These variations resemble real-world phenomena such as chemical morphogenesis, ecological dispersal, and even neural patterning in biological systems.
This piece invites the viewer to see the hidden mathematics that shape the world—how randomness and structure coexist to create complexity in nature.
The painting “Fibonacci in Egypt” was inspired by the Fibonacci sequence and the golden ratio, which are fundamental mathematical concepts that appear through nature and art. At first glance, the patterns may seem chaotic, yet they project a sense of harmony. This is no mere coincidence, as each dot and floral element is arranged and coloured according to Fibonacci numbers. These numbers govern growth and structure in nature, appearing in everything from flower petals and seashells to ocean waves and the spirals of galaxies.
A deliberate mathematical reference is embedded within the painting: there are precisely 618 dots, a direct reference to 0.618, the inverse of the golden ratio. This ratio has long been associated with balance and beauty in both art and nature. Through this work, I aim to highlight how mathematical principles shape our world, revealing the elegance of structured randomness and the universality of these mathematical patterns.