**A
high moutain
**a
fractal surface

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 ! (4^{7})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
4^{6}). Clicking again in TRIANGLE, you will be
back to the initial triangle. |

**Fractal figures generated
using L-systems**** **