How does it work?

Shapes of mountains and clouds are really fractals of a certain kind if you think in general enough terms:

A fractal is geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.

Looking in nature, the shapes of mountains and clouds fit this definition. As you see in the applet above, it is possible to model their shapes and evolution quite well by using a simple algorithm which literally creates a fractal pattern.

The generation algorithm is almost the same as for mountains as for clouds. Both of them are generated by a recursive procedure that picks random values for the corners of some simple shape. Using those values, the polygon is "fractured". Since each of the fractured pieces is approximately a reduced-size copy of the original shape, we can repeat the procedure by further fracturing the pieces, and so on.

The main difference between the cloud algorithm and the mountain algorithm is that the fractured shape for mountain generation is a triangle and each value stands for altitude, whereas the fractured shape for clouds is a rectangle and each node's value should be transformed to color. Random values are averaged with nearest nodes' values so both rock surface and clouds look sufficiently smooth.

More details, references and software are available online.

What is going on?

At the top part of the applet there is a panel containing three groups of check boxes (such grouped check boxes are known as option buttons or radio buttons).

1. The first group includes two buttons, labeled Run and Stop . We can use these buttons for running and stopping the animation.

2. The second group has label Degree and includes three buttons labeled 5, 6 and 7 respectively. Degree stands for degree of number 2 and this value corresponds with the number of segments each side of primary triangle or rectangle is divided to.

Each next degree corresponds with two times more number of segments and four times more number of triangles and rectangles then previous one.

3. The third group has label Light and includes two buttons labeled Rear and Front respectively. Each of them sets its own (rear and front) direction of lighting.

Felix Golubov.

E-mail: FGolubov@aol.com