Galaxy - recursive geometry poster

SERIES C // Structure

Galaxy

€39

Every ray curls the same way, until the sound becomes a spiral galaxy.

Colour
Format
Size

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About the piece

Sound that builds. Thousands of blocks of light grow by a set of recursive rules - branching, bending and repeating until the signal fades. The architecture of a single moment. Perlin noise explained

Drawn in code from seed
00004
Series
Structure
Variant
Spiral
Palette
Violet
Sizing

30 × 40 cm (12 × 16 in) or 45 × 60 cm (18 × 24 in), with a white border around the picture. Framed prints come in a black or natural wood frame (12 mm wide) with plexiglass, ready to hang.

Print & materials

Fine art matte paper (200 gsm) at 300 DPI, made to order. Every size is rendered natively - lines stay razor-sharp even at the largest size.

Shipping & payment

Free shipping worldwide. Every print is made to order within a few business days and shipped worldwide, packed to arrive flawless. You see the delivery estimate for your country when you order.

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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.

The story

The same rules as Transmitter, with one change: each new block turns a little further in the same direction. A hundred and twenty rays bend into spiral arms this way. Real spiral galaxies, like the Milky Way, owe their arms to density waves.

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
spoke → box · spoke(x + 2, rz ± 0.4°, s × 1.035)   p = 90%spoke → box · spoke(rz + θ, s × 0.8) · spoke(rz − θ, s × 0.8)   p = 5%spoke → node · arc · arc · spoke   p = 3%arc → box · arc(rz = step / r)s(t) = Σₖ aₖ·(½ + ½·sin(2π·fₖ·t + φₖ)) · Σⱼ bⱼ·e^(−((t − cⱼ)/wⱼ)²)
Parameters
Rays
120
Cores
1
Curl (°/step)
3.4
Object limit
14,000
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
Shapes drawn
3,358
Blocks
3,287
Nodes
71
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

  1. 1956

    Noam Chomsky describes formal grammars: a finite set of rules that can generate infinitely many sentences.

  2. 1968

    Biologist Aristid Lindenmayer applies the same idea to plants. His L-systems describe how branches grow using rewriting rules.

  3. 2005

    Context Free Art brings grammars into art: a picture is a program of a few rules that call themselves.

  4. 2007

    Mikael Hvidtfeldt Christensen releases Structure Synth, extending grammars into three dimensions. This series grows from there.

Perlin noise

  1. 1982

    Ken Perlin works on the effects for the film Tron and is frustrated that computer images look too "machine-like".

  2. 1983

    Perlin invents his noise and publishes it in 1985 at SIGGRAPH, in the paper "An Image Synthesizer".

  3. 1997

    Perlin receives an Academy Award for Technical Achievement: his noise becomes the basis of smoke, fire and cloud textures in film.

  4. 2001

    Perlin publishes an improved version and "simplex" noise. Today games, films and programmer art all over the world use it.

In nature

Recursive rules for plant growth were first written down in 1968 by biologist Aristid Lindenmayer, watching algae: a cell divides, and each new branch repeats the old one.