Zio Chris' De Jong Attractor by Chris Culy

is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The de Jong attractor^{?} is another example of a fractal. Like the
Lorenz attractor and unlike tthe
Mandelbrot set and
the Burning Ship fractal, here we have four parameters
that we can adjust to get different images. There is no standard approach to coloring; below are
some examples. As with the other fractal examples, this page draws heavily on
an example on Paul Bourke's
wonderful site.

The de Jong attractor is constructed differently from
the Mandelbrot set and the Burning Ship fractal, which we have already seen.
In those two fractals, we calculated sequences of points, based on a starting point, and we then
colored the starting point based on how many times it took for the points in the sequence to
reach a certain size. However, in the de Jong attractor, we always start from the origin (so there
is only one sequence) but we plot *every* point in the sequence. Here are the formula for
the sequence.

nextX = sin(a * previousY) - cos(b * previousX);

nextY = sin(c * previousX) - cos(d * previousY);

Now we have 4 **parameters**: *a, b, c, d*. By varying the values we assign to
these parameters we get different shapes. For details, look at the function drawDeJong().

There is no standard approach to coloring the sequence. We might have a single color, or we might
use the distance between successive points to give a shade of color, or a color of the rainbow.
For examples, look at the functions getBlue(), getRedShades(), getRainbow().

Color schemes:
Some examples:

a:
b:
c:
d:

Density (denser is slower):

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