I Built a Generative Art Machine Around One Number: 1.618
An experiment in mathematics, artistic composition, controlled randomness, and the idea that the instructions can be as important as the artwork.
There’s something slightly suspicious about the way people talk about the golden ratio.
The number 1.618 is regularly presented as though it holds a secret formula for beauty. Apply the right proportions, position a subject at the right intersection, add a golden spiral, and apparently everything falls into place.
But what happens when you ask the mathematics to do more than provide a decorative overlay?
What if you give it responsibility for the entire composition?
That’s the question behind ALGO/ART, a browser-based generative art system I’ve been developing.
The idea becomes the machine
The conceptual artist Sol LeWitt argued that an idea could become a machine for making art.
It’s a compelling proposition because it moves the creative decision away from the individual mark and towards the system that produces it.
Rather than deciding exactly where every line should go, you establish rules. The artwork becomes one possible outcome of those instructions.
I wanted to explore that principle using code.
ALGO/ART doesn’t use a trained image-generation model. It doesn’t need a text prompt describing what a picture should contain. Instead, it uses explicitly programmed mathematical relationships, composition rules and a deterministic random-number generator.
The machine knows nothing about aesthetics in the human sense. It has no appreciation of balance, tension, rhythm or beauty. But we can attempt to describe some of those concepts mathematically.
And that’s where things get interesting.
One mathematical language, eight different systems
At the centre of ALGO/ART is the golden ratio, represented by the Greek letter φ (phi):
φ ≈ 1.6180339887
Its related proportions, approximately 61.8% and 38.2%, provide a framework for dividing space, organising visual hierarchy and distributing elements across a canvas. The golden angle, approximately 137.5°, introduces another way of organising rotations, radial structures and organic growth.
But I didn’t want the generator to produce endless variations of the same golden spiral.
Instead, ALGO/ART contains eight different generative systems. Some build arrangements of shapes and evaluate their visual relationships. Others divide the canvas recursively, construct geometric forms, create networks, grow branching structures or organise marks along curved trajectories.
Each system interprets the same mathematical language differently.
Eight systems, one mathematical language
Each of ALGO/ART’s eight systems interprets the golden ratio (φ ≈ 1.618) differently, using its proportions (61.8% and 38.2%), the golden angle (137.5°), or φ-based scaling to organise compositions.
- Orbital Studies generates several candidate layouts, positioning important elements near golden-ratio focal points (38.2% and 61.8% across the canvas). It scales shapes according to φ, evaluates their hierarchy, spacing and negative space, and selects the strongest composition.
- Golden Trajectories uses φ to organise movement across the canvas. Logarithmic spirals provide a mathematical foundation, while golden-ratio focal points, golden-angle rotations and φ-scaled distances guide sweeping curves, fans, intersecting paths and cascading forms.
- Recursive Divisions repeatedly splits the canvas at approximately 61.8% or 38.2%, creating progressively smaller territories. Nested forms can shrink by 1/φ, producing a hierarchy of related rectangles and shapes.
- Radiant Systems positions one or more hubs around golden-ratio focal points, then distributes shapes using the golden angle of approximately 137.5°. Radial distances and element sizes follow φ-related proportions, creating structured but uneven bursts.
- Connected Fields arranges nodes using golden-ratio positions and a hierarchy of large, medium and small elements. Connections favour φ-related distances while limiting unnecessary crossings, so the mathematics influences both the placement of shapes and the relationships between them.
- Growth Systems creates branching structures whose lengths decrease by approximately 1/φ (0.618) with each generation. Branching directions draw on the golden angle, producing progressively smaller, organically arranged forms.
- Constructed Forms creates Bauhaus- and Suprematist-inspired compositions using independent geometric shapes. Their positions favour golden-ratio intersections, their sizes follow φ-based scales, and their rotations and spacing use golden-angle and φ-related relationships.
- Automatic Marks organises apparently spontaneous strokes into territories positioned using golden-ratio proportions. Territory sizes and stroke lengths are φ-scaled, while golden-angle turns influence directional flow, creating controlled irregularity around deliberately protected empty spaces.
The importance of what isn’t there
One of the more interesting problems was negative space.
A computer is perfectly capable of filling a canvas with thousands of marks. That doesn’t mean the result is a compelling composition.
Sometimes the most important part of an artwork is the area deliberately left empty.
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ALGO/ART therefore considers not only the placement and scale of elements, but also the spaces between them. Some compositions protect empty regions. Others deliberately push activity towards the edges or create tension between opposing forms.
The mathematics proposes relationships, but those relationships still need to be translated into meaningful visual decisions. And more geometry doesn’t automatically produce better art.
Making mathematical precision feel imperfect
Once the composition exists, there’s another problem.
Computer-generated geometry can be almost unnaturally precise. Lines are straight. Circles are perfect. Curves follow their equations without hesitation.
I wanted something different.
ALGO/ART separates composition from rendering. The first part determines where marks belong, how large they should be and how they relate to the available space. The second decides how those marks actually appear.
The marker-rendering engine introduces wobble, variations in pressure, repeated strokes, uneven opacity and dry-ink effects.
The underlying structure remains mathematical, but the surface becomes less mechanically perfect.
It’s an intentionally contradictory approach.
Mathematics sets the rules. The marker breaks them.
Of course, the imperfections are themselves generated by code. No actual human hand is moving the pen. But that contradiction is part of the experiment: can explicitly programmed irregularity create something that feels less precise than the system responsible for producing it?
Randomness you can reproduce
ALGO/ART also uses deterministic seeds.
That means an artwork isn’t just a fleeting arrangement produced by an unpredictable random-number generator. Its state can be recreated.
The same renderer version, seed and settings generate the same artwork state.
You can alter the parameters, change how strongly the golden ratio influences the arrangement, modify the density or experiment with different rendering characteristics. You can also share a link that opens the artwork directly in the editor with its settings preserved.
The image becomes more than a finished object. It becomes an editable set of instructions.
This is probably the aspect of the project that interests me most: the artwork and its method of construction are inseparable.
A gallery of experiments
I’ve also built an automated daily gallery. Each day, the system generates a collection of new studies using its different algorithms, with reproducible settings and links back to the editor.
Explore the ALGO/ART Daily Gallery
I like the idea of these images accumulating over time. Not as a collection of masterpieces, but as an archive of what happens when the same underlying mathematical principles are repeatedly interpreted in different ways.
Some results are more convincing than others. That’s important. A mathematical system shouldn’t be mistaken for a guarantee of artistic quality.
The golden ratio is a compositional tool, not a universal law of beauty. There are still decisions about what works, what doesn’t, what’s surprising and what’s worth keeping.
Those decisions belong to the person looking at the work.
So who is actually making the art?
Is it the programmer who defines the rules? The system that executes them? The person who adjusts the parameters? Or the viewer who decides whether the result is interesting?
I don’t think these questions have especially neat answers.
But they become more relevant as creative software increasingly automates processes that were once exclusively associated with human artistic practice.
ALGO/ART isn’t an attempt to prove that mathematics makes better art, or that computers can replace artists. It’s an attempt to explore what happens when artistic ideas become executable instructions.
The computer can generate the marks. The mathematics can propose the structure. But neither can tell us why a particular arrangement should matter.
And perhaps that’s where the most interesting part of art still begins.
ALGO/ART is free to experiment with in your browser.
Open the generator · Explore the daily gallery · View the source code on GitHub
Mathematics sets the rules. The marker breaks them.
