A high moutain
a fractal surface
an applet made by António Miguel de Campos (Portugal)

 

Click in CHANGE LEVEL button. Moving the mouse on top of the screen you can change the point of observation of the surface. The x-axis is in red, the y-axis in yellow, and the z-axis in blue. Notice that, at level 7, there are 16384 triangles ! (47)

The midpoints of the 3 lines of each triangle are found and are moved up or down (randomly) within a certain range of values. Four triangles are generated from each original triangle. The same procedure is repeated 6 or 7 times but each time moving the midpoints within a range of values which is half of the previous one.

The final surface has a fractal dimension (Hausdorff Besicovitch dimension) which is greater than 2 and smaller than 2.358 ( ln(4)/ln(1.8) ), because in each iteration 4 triangles are generated from each original triangle, which is less than 1.8 times larger than them.

If you click in PIRAMID , you see the evolution from a piramid. Notice that, in this case, at level 6 you also have already 16384 triangles ! (4 times 46). Clicking again in TRIANGLE, you will be back to the initial triangle.

Fractal figures generated using L-systems 

A fractal leaf and the Sierpinski triangle