The border regions around primary Mandelbrot sets hide an infinite number of pleasing fractal images. Occasionally they are called chaotic images, but in this context chaos differs from the meaning it has in colloquial English. It does not mean total confusion nor random chance. No, this kind of chaos knows rigid rules, but we do not understand them.

Animated by presentations on the Internet *) I thought about possibilities to create three-dimensional presentations without too much effort: During calculation the computer holds a structure in width, depth and height and since the third dimension (height) can not be presented on the computer screen colors are used instead. But if we incline that structure back this height may be projected to the plane; basically one might do without colors, but coloring does not disfigure the picture.

Turning the 2D-picture seemed to be a good idea, but an illumination (with shadows) seemed essential. So I copied my 2D-sources and added the required routines.

Let us switch to natural surroundings: Weather situations follow chaotic rules and the next image shows, how easily one can get lost in chaos:

Moving from A to B you are on a rather regularly rising slope: The terraces you see are due to the fact that here only some 100 color- i.e. level-gradations are used; in reality the terraces do not exist.

So from A to B you may, using an appropriate extrapolation method, foresee the position of the next dots rather successfully. But when going from B to C your method will fail; or even worse: nobody can tell you why and where those "trees" rise up.

The picture shows why i.e. weather forecasts occasionally may be false, although a very subtle extrapolation method is used. I do not say, how forecasts are to be improved, I only illustrate, how easily mistakes or misinterpretations may happen.

*) I am sorry, but I can not recall the place where I found those pictures. Hoping the respective author is not too much offended, I present them hear anyway.