The story
Three ribbons, 210 threads, each with its own phase shift. A stream of water falls smooth at first, then breaks into drops: this is called the Plateau-Rayleigh instability.
Fine art paper
200 gsm enhanced matte
Printed on thick uncoated art paper at 300 DPI. Rich colour, razor-sharp lines, no glare.
Real wood frames
Black or natural wood
Wooden frame, 22 mm deep, with plexiglass that is lighter and safer than glass. Arrives ready to hang.
Made to order
Free shipping worldwide
Each print is made for you when you order and packed to arrive flawless, wherever you are.
MATHEMATICS
The maths behind the picture
Every piece is computed, not drawn. These are the real equations and numbers from the program that made this exact piece.
Read the guide: Perlin noise explained →Equations
P(t, φ) = C(t) + h(t)·sin φ·(cos θ(t)·N + 0.35·sin θ(t)·T)θ(t) = 2π·k·t + θ₀ + 1.4·noise(3t)h(t) = w₀ + w₁·s(t)^1.1s(t) = Σₖ aₖ·(½ + ½·sin(2π·fₖ·t + φₖ)) · Σⱼ bⱼ·e^(−((t − cⱼ)/wⱼ)²)
Parameters
- Ribbons
- 3
- Lines
- 210
- Twists
- 1.841
- Meander
- 2.049
- Signal frequencies
- 5.802 · 15.055 · 3.086 · 14.985
- Swells
- 0.692±0.209 · 0.32±0.132 · 0.192±0.12
- Perlin noise
- 4 octaves · falloff 0.5
Measured while drawing
- Samples
- 147,210
- Signal peak (t)
- 0.295
What these numbers mean
The form is driven by a sound signal made of the frequencies 5.802 · 15.055 · 3.086 · 14.985. Where the signal is louder, the structure grows further.
Nature is neither perfectly smooth nor completely random: clouds, mountains and waves are somewhere in between. In 1983 Ken Perlin invented a noise that looks like nature: a smooth function that gives random but gentle changes. The program adds four layers (octaves) of this noise, each half as strong and twice as fine as the last. That is what gives the lines life, so they don't look like they were drawn with a ruler.
HISTORY
Where this idea comes from
- 1847
Jean Frenet (1847) and Joseph Serret (1851) independently describe how orientation changes along a curve in space: tangent, normal and binormal.
- 1960s
Early computer artists such as Frieder Nake and Georg Nees use plotters to draw lines defined by equations.
- today
Parametric surfaces are the basis of 3D graphics, from cars to animation. Here one such surface becomes a ribbon of light.
Perlin noise
- 1982
Ken Perlin works on the effects for the film Tron and is frustrated that computer images look too "machine-like".
- 1983
Perlin invents his noise and publishes it in 1985 at SIGGRAPH, in the paper "An Image Synthesizer".
- 1997
Perlin receives an Academy Award for Technical Achievement: his noise becomes the basis of smoke, fire and cloud textures in film.
- 2001
Perlin publishes an improved version and "simplex" noise. Today games, films and programmer art all over the world use it.
In nature
The ribbons twist into helices, like the tendrils of beans and vines. In 1865 Charles Darwin wrote a whole paper on how climbing plants coil.
Follow along
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