3D Fractals in stereographic representation

These images must be looked at in a special manner (crossed eye view) to see them three dimensional. (Really three dimensional, not a 2D projection of a 3D obejct!)
For description there is a section below taken from the Quat 0.92 documentation (Quat is the program used for generating these images).

By the way: By clicking on the images you can download the ini file which you can use for generation of the fractal yourself (with Quat 0.92)

3d stereo fractal image

Perhaps you know from the "Magic Eye" books that special ways to look at something (without any additional equipment like 3d glasses) can produce very amazing three dimensional perceptions. The principle used by Quat is different from that of the "Magic Eye" books (Autostereograms), but in my opinion it is easier to learn and achieves great results!
The principle is as follows: Two images seen from two slightly different points are calculated and displayed next to each other. The image to the right is for the left eye, the image to the left for the right eye. (Thus the name "cross eyed").

3d stereo fractal image

If you hold your thumb in ca. 10 cm distance in front of your eyes and look at it as usual, you'll remark that you see the background twice. This is what the principle builds on.

3d stereo fractal image

Look at the example image above. Sit in front of the screen at the distance you usually work at, and then hold your thumb between screen and your eyes (nearer to the eyes than to the screen). You should sit straight in front of the screen, not incline your head and not look from beside at the screen. Now look at the thumb as usual. Pay attention to the images on the screen (without looking at them directly, always look at the thumb!)
If you see four images now, then the thumb is too near to the eyes. Move it a bit further away from the eyes and look at it again as usual, while paying attention to the background. Change the distance thumb-eyes until you only see three images. Now the one in the middle is seen three dimensional, but perhaps not sharp. To get a sharp image is a matter of concentration, with increasing experience it gets easier. Watch the non-sharp image for a while (but don't look at it directly). There'll be a point at which mind begins to recognize, that the data that it gets, make really sense and it tries to make it sharp. For some people this process is a bit difficult (as it was for me), others have no problem with it.
If you get used to this kind of viewing, you won't need the help of the thumb anymore.

3d stereo fractal image

By the way, this way to view is not an exotic feature of Quat, in the Internet such stereo images are widely used. This way it is possible to display a photograph of a landscape three dimensionally, for example


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