Ducks Fractals Variations

After getting the Ducks Fractal algorithm working, I tried some variations to see what other kinds of images can be prduced using similar methods.

Using the info from Algorithmic Worlds the basic code within each pixels iteration loop is as follows;

if z.y>0 then z.y:=-z.y;
z.x:=z.x+c.x;
z.y:=z.y+c.y;
z:=Cln(z);

The first line converts Z into its complex conjugate if the imaginary component is greater than 0.
The next 2 lines add the constant C to Z.
The last line takes the log of Z.

Those steps result in z = log(Iabs(z)+p) as stated in the Algorithmic World’s blog post linked above and result in images like the following.

Ducks Fractal

Ducks Fractal

Ducks Fractal

Ducks Fractal

Variation 1 uses the following code;

if z.y>0 then z.y:=-z.y;
z.x:=z.x+c.x;
z.y:=z.y+c.y;
z:=Cln(CSin(z));

CSin is complex Sin.

Here are a few example images from using this method.

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Variation 2 uses the following code;

if z.y>0 then z.y:=-z.y;
z.x:=z.x+c.x;
z.y:=z.y+c.y;
z:=Cln(Csub(z,CSec(z)));

CSub is complex subtraction and CSec is the complex cosecant.

Here are a few example images from using this method.

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Ducks FRactal Variation

Variation 3 uses the following code;

if z.y>0 then z.y:=-z.y;
z:=CSin(z);
z.x:=z.x+c.x;
z.y:=z.y+c.y;
z:=Cln(z);

Here are a few example images from using this method.

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Variation 4 uses the following code;

if z.y>0 then z.y:=-z.y;
z.x:=z.x+c.x;
z.y:=z.y+c.y;
z:=Cln(CSqr(z));

CSqr is the Z squared.

Here are a few example images from using this method.

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

Ducks Fractal Variation

All of the above images can (and really need to) be seen in much more detail high resolution images in my flickr gallery.

Ducks Fractals are now included with Visions Of Chaos.

Jason.

2 responses to “Ducks Fractals Variations

  1. Pingback: Wonderful, Beautiful Fractals – Anders Franz Terkelsen's blog

  2. Wow, this is really incredible! These image have a certain pixel-perfect quality that I really like. Keep up the good work!

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