Thomas - strange attractor poster

SERIES A // Attractors

Thomas

€39

A particle in a labyrinth of sine waves. The simplest possible equations, the most tangled possible path.

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About the piece

Chaos has a shape. Each picture is the path of a single point through space, computed hundreds of thousands of times by the same equations. What is a strange attractor?

Drawn in code from seed
00002
Series
Attractors
Variant
Thomas
Palette
Aurora
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

Belgian biologist René Thomas published these equations in 1999 while studying feedback loops in living cells: one gene holding back another, which holds back a third. He called it "labyrinth chaos". Three sines in a circle and one friction parameter b: the smaller b, the deeper the path wanders.

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 strange attractor? →
Equations
dx/dt = sin y − bxdy/dt = sin z − bydz/dt = sin x − bz
Parameters
System
Thomas
b
0.18
Measured while drawing
Start point
4.107, 0.76, -1.164
Time step
0.03
Integration steps
420,000
Method
RK4
Lyapunov exponent λ
0.034
View angle
85.3° / -4.1° / -14.3°
Coverage (%)
19.4
What these numbers mean

λ = 0.034 > 0 means chaos: two paths starting 0.00000001 apart separate by a factor of e^(0.034·t). Their distance doubles every 20.39 time units, so very soon they have nothing in common.

HISTORY

Where this idea comes from

  1. 1890

    Henri Poincaré, working on the three-body problem, first glimpses chaos: a tiny change at the start changes the whole outcome.

  2. 1963

    Edward Lorenz at MIT reduces a model of the atmosphere to three equations and finds that weather cannot be predicted far ahead.

  3. 1971

    David Ruelle and Floris Takens coin the term "strange attractor".

  4. 1972

    Lorenz's talk "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" gives the butterfly effect its name.

In nature

Lorenz's equations describe warm air rising, cooling and falling, the same motion that builds storm clouds in summer.