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.
zₙ₊₁ = zₙ² + cz₀ = 0|zₙ| > 2 ⇒ c ∉ M- Re(c) centre
- -0.761629
- Im(c) centre
- -0.084758
- Window width
- 0.0035
- Magnification ×
- 885.7
- Max iterations
- 1,400
- Rotation
- -15.1°
- Points computed
- 1,533,070
- Inside the set (%)
- 2.22
- Mean escape
- 147.6
This window is magnified 886 times. 2.2% of points stay trapped in the set forever; the rest escape after 148 steps on average. Each point's colour is exactly that step count.
HISTORY
Where this idea comes from
Mandelbrot
- 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.
