Go ahead and play with the fractal, just remember one thing, as you move from iteration to iteration, it will take longer and longer to draw. At some point you will probably run out of memory3.
This applet was written using the L-system method described in the previous section. It gets initialized with an axiom and a production rule. Every time you click on the button to go to the next iteration, it figures out a new string by replacing the production rule into the current string. It then proceeds to draw the new iteration onto the screen. This applet is implemented in such a way that you can see the fractal as it gets drawn. In the last section of this fractal lessons there is a few more L-system based fractals for your enjoyment!
Now a few questions for you. The first one related to how this fractal is implemented.
If you check carefully, you'll notice that the lengths of the lines are smaller with each iteration. The length of the lines gets resized to exactly 1/3rd to maintain the overall size constant. Check it out! Now that you agree that the overall area doesn't change, lets figure out what happens to the total length of the lines. Can you complete the following table?
| Iteration | Total Length |
| 0 | 1 |
| 1 | ? |
| 2 | ? |
| 3 | ? |
| 4 | ? |
| 5 | ? |
| 6 | ? |
Now lets go to the next applet, the Sierpinski
Triangle Java applet.