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.
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)- 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
- Shapes drawn
- 3,358
- Blocks
- 3,287
- Nodes
- 71
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
Structure
- 1956
Noam Chomsky describes formal grammars: a finite set of rules that can generate infinitely many sentences.
- 1968
Biologist Aristid Lindenmayer applies the same idea to plants. His L-systems describe how branches grow using rewriting rules.
- 2005
Context Free Art brings grammars into art: a picture is a program of a few rules that call themselves.
- 2007
Mikael Hvidtfeldt Christensen releases Structure Synth, extending grammars into three dimensions. This series grows from there.
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 code art all over the world use it.
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