Fractal Planet
Author: Felix Golubov,
Warner Music Group
E-mail: [email protected]
How does it work?
We consider fractal planet to be a fractal landscape, made upon a sphere. It is absolutely clear how we can build fractal landscape upon the plain triangular net.
To generate a landscape, we "bend" each of the edges of some triangle by raising or lowering the midpoint by some random amount. Then we divide the triangle into four ones by drawing lines between each of the three midpoints. If we apply the same procedure recursively for each new triangle, soon we will get a fractal landscape. See our Fractal Landscape Generator.
To generate a fractal planet, this approach should be slightly changed. We can approximate to sphere with any precision by replacing it with sequence of polyhedrons. Let us include some simple polyhedron having triangular faces into sphere and draw lines between the center of the sphere and midpoint of each edge of each polyhedrons face. Extending each line until it intersect surface of the sphere and drawing lines between points of intersection, we can replace each polyhedrons triangular face with four new faces. Applying this algorithm recursively for each new face, we'll end up with 3-dimensional triangular net of any density we need for. And since we have the algorithm for replacing one triangle with four ones, we can apply here well-known algorithm for fractal landscape generation. The only problem is to choose a proper polyhedron we should start from. Of course, we could use tetrahedron, but in that case all new small faces, situated near each of four primary tetrahedron's vertices, would have their biggest angles equal almost 120º. It causes some significant deviations of planet's shape. As result, any planet, generated by our algorithm, would have much more predetermined and less casual pattern of shape than it should be. It means we should start our algorithm from either octahedron or icosahedron as well. In the Java-applet, you can see here, the fractal generating algorithm starts from octahedron, but another solution is quite possible.
What is going on?
At the top part of the applet there is a panel containing two groups of option buttons and one check box.
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 4, 5 and 6 respectively. This value indicates a power of 2 and corresponds with the number of segments each edge of primary octahedron is replaced with.
| Degree | 4 | 5 | 6 |
| Num.segm. | 16 | 32 | 64 |
Each next degree corresponds with two times more number of segments and four times more number of triangular faces then previous one.
3. There is separated check box labeled Changing. When it is selected, the shape of planet surface is changing continuously, otherwise it remains unchanging.
Felix Golubov.
E-mail: [email protected]