SERIES I // FRACTAL FLAME

Fractal flame posters

Light like smoke and silk. Millions of points jump between a few rules chosen at random, and their traces build shapes no hand would draw.

Read the guide: What is a fractal flame? →
All 58 Attractors 12 Mandelbrot 6 Flame 4 Structure 6 Flux 6 City 6 Ridges 6 Orbit 6 Hopf 4 Objects 2
Flame - Feathers Feathers Flame from €39 Flame - Smoke Smoke Flame from €39 Flame - Rose Rose Flame from €39 Flame - Pinwheel Pinwheel Flame from €39

MATHEMATICS

The maths behind the picture

  1. 01

    The chaos game

    A point jumps millions of times, and at each jump it picks one of a few rules at random. Where it lands most often, the image glows brightest. Scott Draves devised the method in 1992.

    xₙ₊₁ = Fᵢ(xₙ), i random
  2. 02

    Non-linear variations

    Each rule is a shift and a turn, then a bend by one of several functions: sine, sphere, swirl, spiral. They make the shapes soft as smoke and silk.

    F(x) = Σ wⱼ·Vⱼ(Ax + b)
  3. 03

    Colour from history

    Each point remembers which rules it used last, and that history becomes its colour. Brightness is logarithmic, so even the faintest traces show.

    L = log(1 + n) / log(1 + nₘₐₓ)

HISTORY

Where this idea comes from

  1. 1981

    John Hutchinson describes iterated function systems: a fractal as a set of rules that repeat.

  2. 1988

    Michael Barnsley shows that a few rules and the chaos game draw ferns and clouds.

  3. 1992

    Scott Draves devises the fractal flame: non-linear variations, log density and colour from history.

  4. today

    The flame is one of the best-known forms of programmer art. Here every piece has its own rules and its own number.

In nature

The flame descends from Barnsley's fern of 1988: a few rules, picked at random, draw a leaf down to its last vein.