SERIES F // FIRST SIGNALS - STACKED SPECTRA
Гребени · Ridges
Where it all began. Dozens of waveforms stacked one behind another, like a landscape captured by a radio telescope at 3 a.m.
MATHEMATICS
The maths behind the picture
- 01
Stacked spectra
Each line is one moment of sound. The lines are stacked one behind another and each hides the ones behind it, like a mountain range seen from far away.
yᵢ(t) = bᵢ − A·env(t)·signal(t) - 02
The envelope
Gaussian envelopes decide where the signal is strong: peaks rise in the middle of the picture and fade towards the edges.
env(t) = Σₖ aₖ·e^(−((t − cₖ)/wₖ)²) - 03
Noise and carrier
Inside the envelope a carrier frequency oscillates, and Perlin noise acts as the natural irregularity of sound, so no two lines are alike.
|sin(2π·f·t + φᵢ)|³ · noise(t) - 04
Perlin noise
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.
noise(x) = Σₖ 0.5ᵏ · perlin(2ᵏ·x), k = 0…3
HISTORY
Where this idea comes from
Ridges
- 1809
Carl Friedrich Gauss publishes the bell-shaped distribution. Every mountain in these pictures is one Gaussian envelope.
- 1967
Jocelyn Bell Burnell discovers the first pulsar. Pulsar signals were plotted exactly like this, as stacked lines, pulse after pulse.
- 1983
Ken Perlin invents the noise that gives these lines their natural irregularity.
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.