Learning from Vera Molnár — Study 01: Multiplication
When people look at early computer-generated art, it’s easy to focus on the finished image. What interests me is the thinking that produced it.
This project marks the beginning of a series inspired by the methods of Vera Molnár, one of the pioneers of computational art. Rather than attempting to recreate her work, I’m exploring the kinds of mathematical systems that shaped it. The aim isn’t imitation; it’s understanding.
To do that, I’ve imposed a number of deliberate constraints. Every study in this series will begin with a simple mathematical rule and a minimal visual language. The artwork should emerge from the logic of the system, not from decoration or visual effects.
Starting with the simplest possible system
For the first study I wanted to use the smallest possible set of ingredients.
- A3 portrait format
- A regular grid
- One line positioned in the centre of every square
- Black lines on an off-white background
- No colour
- No animation
- No randomness
- One mathematical operation
Nothing more.
The challenge was to discover whether something visually interesting could emerge from almost nothing.
Why multiplication?
Multiplication is one of the most fundamental operations in mathematics.
Unlike randomness or noise, multiplication is entirely deterministic. Given the same two numbers, it will always produce the same result. That predictability makes it an ideal starting point when exploring algorithmic drawing.
Every line in the composition is positioned according to its location within the grid.
Each square has two values:
- its column number
- its row number
Those two numbers are multiplied together.
Angle = Column × RowThat single calculation determines the orientation of every line on the page.
There are no exceptions.
No adjustments.
No artistic intervention once the rule has been defined.
From arithmetic to drawing
If we imagine the grid beginning in the top-left corner, the first few values are surprisingly simple.
| Column | Row | Multiplication |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 0 |
| 2 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 4 |
| 4 | 3 | 12 |
| 8 | 6 | 48 |
| 11 | 15 | 165 |
Those results are then interpreted as rotation angles.
Small numbers produce only slight changes.
As the values increase, the lines rotate further.
Although the underlying calculation remains extremely simple, the visual complexity gradually increases across the page.
Nothing has been randomised.
The pattern is entirely generated by elementary arithmetic.
The invisible grid
One of the most important decisions was not what to draw, but what not to draw.
The square grid exists only as a mathematical structure.
It isn’t printed.
The viewer never sees it.
Instead, it acts as an invisible coordinate system that provides every line with two pieces of information: its row and its column.
Without the grid there is no calculation.
Without the calculation there is no composition.
The geometry exists before the drawing.
Thinking like an early computer
This project is written in Processing using Java, but the algorithm itself could be described without referring to any programming language.
- Create a grid.
- Number every row.
- Number every column.
- Multiply the row and column numbers.
- Rotate a line by the resulting value.
- Repeat for every square.
That’s the entire system.
Modern software makes it easy to implement, but the underlying idea doesn’t depend on modern computing power. It’s a sequence of instructions that could be described on paper before a single line is programmed.
Constraint as a design tool
One of the things I’m beginning to appreciate is that removing possibilities often leads to stronger ideas.
It’s tempting to add colour, texture or movement, but each additional decision moves the work away from the central question.
Can a single mathematical operation generate a compelling image?
For this study, I wanted the answer to depend entirely on multiplication.
Everything else was intentionally stripped away.
Reflections
Looking at the finished print, I find it interesting that the eye naturally begins to search for order.
Diagonal rhythms begin to appear.
Clusters seem to form.
Some areas feel calm while others become increasingly energetic.
None of those relationships were drawn manually.
They’re simply the visual consequence of applying one rule consistently across an entire system.
Perhaps that’s one of the enduring lessons of early computational art: complexity doesn’t always come from complicated algorithms.
Sometimes it begins with nothing more than a grid, a line, and a single mathematical operation.
Technical Notes
Software: Processing (Java)
Format: A3 portrait
Visual Language:
- Off-white paper
- Black lines
- Invisible square grid
- One centred line per cell
Mathematical Rule:
Angle = Column × Row
A bit of a “what if” idea…
Rather than using identical lines, I wondered what would happen if the basic element became a letter.
The mathematical rule remains unchanged — only the visual language evolves. Each position in the grid is still rotated according to the same calculation, but the line is replaced with a randomly selected alphabetical character.
It’s a small change, yet it introduces a new layer of controlled variation. The randomness only determines which character appears; the underlying system and composition are still governed entirely by the mathematical rule.
Next Study
The next experiment will replace multiplication with a different mathematical operation while keeping every other constraint the same.
The image will change.
The system will remain.