The story
Three equations, each with the product of the other two variables: yz, xz, xy. The path crosses from one vortex to the next, and the four vortices sit in mirrored pairs, like a butterfly's wings.
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.
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
x' = 0,2x + yzy' = 0,01x − 0,4y − xzz' = −z − xy
Parameters
- Seed
- 6
- Method
- RK4
Measured while drawing
- Integration steps
- 340,000
HISTORY
Where this idea comes from
- 1890
Henri Poincaré, working on the three-body problem, first glimpses chaos: a tiny change at the start changes the whole outcome.
- 1963
Edward Lorenz at MIT reduces a model of the atmosphere to three equations and finds that weather cannot be predicted far ahead.
- 1971
David Ruelle and Floris Takens coin the term "strange attractor".
- 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.
Follow along
@rezonanca.art
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