SERIES I // Flame

Smoke

€39

A threefold cloud of smoke around a bright core, with the symmetry of a triangle.

Colour

OriginalInk

Format

Unframed printFramed print

Size

30 × 40 cm45 × 60 cm

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About the piece

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. What is a fractal flame?

Drawn in code from seed: 00003
Series: Flame
Variant: Flame
Palette: Ember

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

A rotation rule of 120° gives the threefold symmetry: every point gets two more copies around the centre. Draves's flame colours each point by the history of rules that brought it there, so each arm of smoke carries its own shade.

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: What is a fractal flame? →

Equations

xₙ₊₁ = Fᵢ(xₙ)F(x) = Σ wⱼ·Vⱼ(Ax + b)L = log(1 + n) / log(1 + nₘₐₓ)

Parameters

Seed: 3

Measured while drawing

Particles: ≈ 10 000 000

HISTORY

Where this idea comes from

1981
John Hutchinson describes iterated function systems: a fractal as a set of rules that repeat.
1988
Michael Barnsley shows that a few rules and the chaos game draw ferns and clouds.
1992
Scott Draves devises the fractal flame: non-linear variations, log density and colour from history.
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.