The Algorithmic Compositions series is an exploration of translating mathematical ideas into visual harmony. The process starts not with colour or emotion, but with a simple line — a single, unbroken path looping over itself until closed. In mathematical terms, such a line defines an Eulerian path, a continuous curve that traverses every edge of a network exactly once before returning to its origin. This deceptively simple idea became the foundation of the series: a set of rules from graph theory transformed into a visual language.
When this line crosses itself, it generates a shape with distinct regions. It can be mathematically shown that it is always possible to colour these regions using only two colours, ensuring that no two adjacent areas share the same hue. (For readers interested in the underlying mathematics, here is a formal proof of this theorem, that we developed together with my uncle, Prof. Yusuf Unlu. For an alternative approach, see this discussion on Math Stack Exchange.)
To construct a composition, I draw three such Euler paths on a single canvas. Each is independent — a separate act of movement and continuity — yet together they form a complex network of overlaps and intersections. After completing the drawing, I photograph it and move to the digital stage of the process. On my iPad, each path becomes a transparent layer, coloured with two tones according to the two-colour rule.
The next step is the algorithmic process that gives these paintings their name. At every point where layers overlap, the colour values are combined according to a mapping rule: the system reads the mixture of the three layers and translates it into a new hue. We can call this a three-dimensional hue, a combination of three colour components, where each component can have only two alternatives. Theoretically, this produces eight distinct colours — each representing all possible combinations of the three binary layers. The resulting image has a strange coherence: it feels deliberate, yet no single decision determines its final form.
The viusal coherence of the iamge stems from the fact that, the colours of neighbouring regions differ only in one dimension. Because only the layer that generates a border and dividing an area into two different areas gives rise to the colour difference in around this border. This gives a sense of continuity and if the viewer is careful, all three layers can be seen separately.
Once the digital model is complete, I return to the canvas. Using acrylics, I manually reconstruct the composition — reintroducing texture, opacity, and the unpredictable subtleties of the brush. This movement between analogue and digital is essential to the work: from canvas to algorithm and back again. Each painting becomes a dialogue between rule and intuition, precision and gesture.
What interests me most is how something emerging from mathematical concepts can lead to visual harmony. The curves are drawn almost randomly (except a few cases where I tried a more figurative approach), yet the outcome is a coherent composition — a balance of repetition, variation, and rhythm. When a viewer spends time with the painting, they begin to sense the structure beneath the surface, distinguishing the three overlapping systems that give rise to the whole.
These works are neither purely digital nor purely handmade. They inhabit a threshold between systems: deterministic yet spontaneous, algorithmic yet tactile. The method guarantees consistency, but the outcome remains unpredictable — each piece grows from the same set of constraints but achieves its own identity.
For me, Algorithmic Compositions is another attempt to create visual representation by borrowing ideas from math and science where the rules are fixed but still allow infinite possibilities. By translating a mathematical structure into colour and form, I believe the beauty of the underlying structure reveals itself in the final composition and becomes something sensuous and alive.