Two-dimensional Fractals in Three-dimensional Space
With this applet, you can enjoy fractals in the three-dimensional
space.
Three-dimensional objects change their appearance smoothly according
to the way we look at them, and some of them are difficult to imagin
from their mathematical definition. The fractals presented here have
fractal dimension 2, and correspondingly, they have three square
projections just as a cube. (One of them have SIX square projections).
You need a Java 2 Plug-in for this applet.
How to use it?
On the upper level of the right panel, there are two comboboxes.
Choose n = 2, 3, 4, or 5 from the left one. Then, you will have, in
the right combobox, a numbering of configurations of n x n cubes out
of n x n x n cubes so that all of them can be seen from the three
surface directions. The figure on the left hand shows such a
configuration (of the form of n levels of n x n squares). Such a
configuration will generate a fractal. Select one of them from the
combobox. The "Next" button will switch to the next configuration.
At the begining, n is set to 2, and there is only one configuration
which will generate the Sierpinski Tetrahedron.
You have the square appearance at the beginning. When you rotate it
three-dimensionally with the arrow buttons, you will have other
appearances of the object. These arrow buttons will rotate the object
with 5 degree. "Go" for continuous rotation, "Stop" to stop,
"Reset" to the the direction at the beginning.