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