SERIES B // Mandelbrot

The Mandelbrot Set

€39

z² + c. The most famous shape in mathematics, an infinite coastline around a single island.

Colour

OriginalRoseInk

Format

Unframed printFramed print

Size

30 × 40 cm45 × 60 cm

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About the piece

One equation, infinitely many coastlines. Each picture is a window into the Mandelbrot set, magnified to places no eye has looked before. The Mandelbrot set explained

Drawn in code from seed: 00001
Series: Mandelbrot
Variant: Full set
Palette: Cyan

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

Robert Brooks and Peter Matelski published the first picture of the set in 1978, typed out in characters on a printer. In 1980 Benoit Mandelbrot made sharper images at IBM, and the set took his name. The whole set fits inside a circle of radius 2, and this is the view of all of it.

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: The Mandelbrot set explained →

Equations

zₙ₊₁ = zₙ² + cz₀ = 0|zₙ| > 2  ⇒  c ∉ M

Parameters

Re(c) centre: -0.698631
Im(c) centre: 0.001578
Window width: 3.1
Magnification ×: 1
Max iterations: 400
Rotation: 0°

Measured while drawing

Points computed: 1,533,070
Inside the set (%): 15.07
Mean escape: 5.9

What these numbers mean

This window is magnified 1 times. 15.1% of points stay trapped in the set forever; the rest escape after 6 steps on average. Each point's colour is exactly that step count.

HISTORY

Where this idea comes from

1918
Gaston Julia and Pierre Fatou study the iteration of complex functions, with no computers, only pencil and paper.
1978
Robert Brooks and Peter Matelski publish the first picture of the set, printed in characters on a line printer.
1980
Benoit Mandelbrot at IBM explores the set by computer and reveals its infinite complexity. He had coined the word "fractal" in 1975.
1982
Adrien Douady and John Hubbard prove the set is connected and name it after Mandelbrot.

In nature

Ferns, romanesco cauliflower and a sea coast share the property of the set's edge: the part looks like the whole. In 1967 Mandelbrot asked how long the coast of Britain is. The answer depends on how finely you measure.