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
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().
a: b: c: d:
Density (denser is slower):