WOLFRAM|DEMONSTRATIONS PROJECT

Peter de Jong Attractors

​
hints
Set "points" low to adjust parameters.
Set "points" high for better image quality.
Browse the bookmarks for the preset pictures.
Animate the bookmarks for a slideshow.
parameters
a
0.56
b
0.53
c
-0.274
d
0.67
points
n
150000
This Demonstration iterates the map attributed to Peter de Jong:
x
n+1
=sin(aπ
y
n
)-cos(bπ
x
n
)
,
y
n+1
=sin(cπ
x
n
)-cos(dπ
y
n
)
.
The coordinates of a random point
(
x
0
,
y
0
)
in the plane is substituted into the formula and evaluated; the result is fed back into the formula and the process is iterated. Such repeated substitution (recursion or iteration) often produces points spreading over beautiful structures called attractors. Thus a simple mathematical rule produces complex visually esthetic images.